Trigonometry : Pythagorean Identities

Study concepts, example questions & explanations for Trigonometry

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Example Questions

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Example Question #11 : Trigonometry

Reduce the following expression.

Possible Answers:

Correct answer:

Explanation:

Because  

therefore:

By definition of cosecant,

Example Question #21 : Trigonometric Identities

Reduce the following expression.

Possible Answers:

Correct answer:

Explanation:

There are several ways to work this problem, but all of them use the second Pythagorean trig identity, .

You can use this identity to substitute for parts of the expression. Here are two examples.

Method 1:

Substituting  for , we get

, which equals zero.

Method 2:

Substituting  for , we get

, which equals zero.

 

Regardless of which substitution you choose, the answer is the same.

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