Using Pythagorean Identities

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Math › Using Pythagorean Identities

Questions 1 - 4

1

Simplify

$\cot(x)\times{\sin(x) }$

$\cos(x)$

$\tan(x)$

$\arcsin(\pi )$

$\csc(x)$

$\arcsin(x)$

Explanation

$\cot(x) = \cos(x)/\sin(x)$ . Thus: $[\cos(x)/\sin(x)]\times\sin(x)=\cos(x)$

2

Simplify:

$\sin^2x+\cos^2x+\tan^2x$

$\sec^2x$

$\sin x\cos x$

$\csc^2 x$

This is the most simplified version.

$2\cos x+\cot x$

Explanation

Whenever you see a trigonometric function squared, start looking for a Pythagorean identity.

The two identities used in this problem are $\sin^2 x + \cos ^2 x=1$ and $\tan^2 x +1 =\sec^2 x$ .

Substitute and solve.

$\sin^2x+\cos^2x+\tan^2x=?$

$(\sin^2x+\cos^2x)+\tan^2x=?$

$(1)+\tan^2x=\sec^2 x$

3

Simplify $\frac{\cos^2x-1}{\sin x}$ .

$-\sin x$

$\sin x\cos x$

$\tan x$

$\sin x$

$\sin^2 x$

Explanation

Remember that $\sin^2x+\cos^2 x=1$ . We can rearrange this to simplify our given equation:

$\frac{\cos^2x-1}{\sin x}$

$=\frac{-\sin^2x}{\sin x}=-\sin x$

4

Simplify

$\frac{cot (x)\cdot tan(x)}{cos(x)}$

$\sec(x)$

$\cos(x)$

$\cos(x)\times\tan(x)$

$\cot(x)/sec(x)$

$\csc(x)$

Explanation

$\cot(x)\times\tan(x) = 1$

and

$1/(\cos(x)) = \sec(x)$ .

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