Precalculus : Proving Trig Identities

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Proving Trig Identities

Simplify:  

Possible Answers:

Correct answer:

Explanation:

To simplify , find the common denominator and multiply the numerator accordingly.

The numerator is an identity.

Substitute the identity and simplify.

 

Example Question #2 : Prove Trigonometric Identities

Evaluate in terms of sines and cosines:  

Possible Answers:

Correct answer:

Explanation:

Convert  into its sines and cosines.

Example Question #1 : Prove Trigonometric Identities

Simplify the following:

Possible Answers:

The expression is already in simplified form

Correct answer:

Explanation:

First factor out sine x.

Notice that a Pythagorean Identity is present.

The identity needed for this problem is: 

Using this identity the equation becomes,

.

 

Example Question #1 : Prove Trigonometric Identities

Simplify the expression 

 

Possible Answers:

Correct answer:

Explanation:

To simplify, use the trigonometric identities  and  to rewrite both halves of the expression:

Then combine using an exponent to simplify:

Example Question #2 : Prove Trigonometric Identities

Simplify 

Possible Answers:

Correct answer:

Explanation:

This expression is a trigonometric identity: 

Example Question #1 : Prove Trigonometric Identities

Simplify 

Possible Answers:

Correct answer:

Explanation:

Factor out 2 from the expression:

Then use the trigonometric identities  and  to rewrite the fractions:

Finally, use the trigonometric identity  to simplify:

Example Question #1 : Prove Trigonometric Identities

Simplify 

Possible Answers:

Correct answer:

Explanation:

Factor out the common   from the expression:

Next, use the trigonometric identify  to simplify:

Then use the identify  to simplify further:

Example Question #1 : Prove Trigonometric Identities

Simplify 

Possible Answers:

Correct answer:

Explanation:

To simplify the expression, separate the fraction into two parts:

The  terms in the first fraction cancel leaving you with:

Then you can deal with the remaining fraction using the rule that . This leaves:

You can separate this into:

And each half of this expression is now a trigonometric identity:  and . This gives you:

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