College Algebra & Trigonometry, 2018a

10.1. RECIPROCAL AND PYTHAGOREAN IDENTITIES 441
Beginning with the original statement:
(sin θ)(cot θ) =cosθ
Replace cot θ with cos θ
sin θ :
(sin θ) cos θ
sin θ =cosθ
Then canceling out the sin θ:
cos θ =cosθ
There are four fundamental approaches to verifying trigonometric identities:
1. write everything in terms of sines and cosines
2. make a common denominator and add fractions
3. split a fraction
4. factor and cancel
Not all of these can be used in every problem and some problems will use combinations
of these strategies. Here is another example.
Example 2
Verify the identity tan θ +cotθ = sec θ csc θ.
First we’ll write everything in terms of sines and cosines:
tan θ +cotθ = sec θ csc θ
sin θ
cos θ +cos θ
sin θ = 1
cos θ · 1
sin θ