Sum and Difference Identities For Cosine - Pre-Calculus

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Question

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

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Answer

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

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Question

Use the sum or difference identity to find the exact value: $cos255^\circ$

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Answer

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

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Question

Is the following equation an identity? $cos(x-\pi)=cos(x)$

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Answer

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

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Question

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

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Answer

Using the identity, we can break up the into and then solve: $\cos 300\cdot \cos 45+\sin 300\cdot \sin 45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ and so the correct answer is $$\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ .

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Question

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

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Answer

Here we break up the into and solve using the sin identity: $\sin 135\cdot \cos 30+\cos 135\cdot \sin 30\rightarrow $\frac{\sqrt{2}$}2{}\cdot $\frac{\sqrt{3}$}2{}+\frac{-\sqrt{2}$}2{}\cdot $\frac{1}{2}\rightarrow $\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ and so here the credited answer is $$\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ .

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Question

Use the sum or difference identity to find the exact value: $cos255^\circ$

Tap to reveal answer

Answer

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

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Question

Is the following equation an identity? $cos(x-\pi)=cos(x)$

Tap to reveal answer

Answer

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

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Question

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Tap to reveal answer

Answer

Using the identity, we can break up the into and then solve: $\cos 300\cdot \cos 45+\sin 300\cdot \sin 45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ and so the correct answer is $$\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ .

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Question

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Tap to reveal answer

Answer

Here we break up the into and solve using the sin identity: $\sin 135\cdot \cos 30+\cos 135\cdot \sin 30\rightarrow $\frac{\sqrt{2}$}2{}\cdot $\frac{\sqrt{3}$}2{}+\frac{-\sqrt{2}$}2{}\cdot $\frac{1}{2}\rightarrow $\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ and so here the credited answer is $$\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ .

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Question

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

Tap to reveal answer

Answer

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

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Question

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

Tap to reveal answer

Answer

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

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Question

Use the sum or difference identity to find the exact value: $cos255^\circ$

Tap to reveal answer

Answer

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

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Question

Is the following equation an identity? $cos(x-\pi)=cos(x)$

Tap to reveal answer

Answer

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

← Didn't Know|Knew It →

Question

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Tap to reveal answer

Answer

Using the identity, we can break up the into and then solve: $\cos 300\cdot \cos 45+\sin 300\cdot \sin 45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ and so the correct answer is $$\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ .

← Didn't Know|Knew It →

Question

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Tap to reveal answer

Answer

Here we break up the into and solve using the sin identity: $\sin 135\cdot \cos 30+\cos 135\cdot \sin 30\rightarrow $\frac{\sqrt{2}$}2{}\cdot $\frac{\sqrt{3}$}2{}+\frac{-\sqrt{2}$}2{}\cdot $\frac{1}{2}\rightarrow $\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ and so here the credited answer is $$\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ .

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Question

Use the sum or difference identity to find the exact value: $cos255^\circ$

Tap to reveal answer

Answer

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

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Question

Is the following equation an identity? $cos(x-\pi)=cos(x)$

Tap to reveal answer

Answer

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

← Didn't Know|Knew It →

Question

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Tap to reveal answer

Answer

Using the identity, we can break up the into and then solve: $\cos 300\cdot \cos 45+\sin 300\cdot \sin 45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ and so the correct answer is $$\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ .

← Didn't Know|Knew It →

Question

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Tap to reveal answer

Answer

Here we break up the into and solve using the sin identity: $\sin 135\cdot \cos 30+\cos 135\cdot \sin 30\rightarrow $\frac{\sqrt{2}$}2{}\cdot $\frac{\sqrt{3}$}2{}+\frac{-\sqrt{2}$}2{}\cdot $\frac{1}{2}\rightarrow $\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ and so here the credited answer is $$\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ .

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Question

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

Tap to reveal answer

Answer

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

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Knew It

Sum and Difference Identities For Cosine - Pre-Calculus

Is the following equation an identity?

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the 255 into and then solve:

Is the following equation an identity?

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the into and then solve: and so the correct answer is .

Use the sum or difference identity to find the exact value of .

Here we break up the into and solve using the sin identity: and so here the credited answer is .

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the 255 into and then solve:

Is the following equation an identity?

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the into and then solve: and so the correct answer is .

Use the sum or difference identity to find the exact value of .

Here we break up the into and solve using the sin identity: and so here the credited answer is .

Is the following equation an identity?

Due to this inequality, this is not an identity.

Is the following equation an identity?

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the 255 into and then solve:

Is the following equation an identity?

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the into and then solve: and so the correct answer is .

Use the sum or difference identity to find the exact value of .

Here we break up the into and solve using the sin identity: and so here the credited answer is .

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the 255 into and then solve:

Is the following equation an identity?

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the into and then solve: and so the correct answer is .

Use the sum or difference identity to find the exact value of .

Here we break up the into and solve using the sin identity: and so here the credited answer is .

Is the following equation an identity?

Due to this inequality, this is not an identity.

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value: $cos255^\circ$

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

Is the following equation an identity? $cos(x-\pi)=cos(x)$

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Use the sum or difference identity to find the exact value: $cos255^\circ$

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

Is the following equation an identity? $cos(x-\pi)=cos(x)$

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value: $cos255^\circ$

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

Is the following equation an identity? $cos(x-\pi)=cos(x)$

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Use the sum or difference identity to find the exact value: $cos255^\circ$

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

Is the following equation an identity? $cos(x-\pi)=cos(x)$

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.