The Pythagorean identities pop up frequently in trig proofs. Pay attention and look for trig functions being squared. Try changing them to a Pythagorean identity and see whether anything interesting happens.
The three Pythagorean identities are
![image0.png](https://www.dummies.com/wp-content/uploads/370419.image0.png)
After you change all trig terms in the expression to sines and cosines, the proof simplifies and makes your job that much easier. For example, follow these steps to prove
![image1.png](https://www.dummies.com/wp-content/uploads/370420.image1.png)
-
Convert all the functions in the equality to sines and cosines.
-
Use the properties of fractions to simplify.
Dividing by a fraction is the same as multiplying by its reciprocal, so
-
Identify the Pythagorean identity on the left side of the equality.
Because sin2 x + cos2 x = 1, you can say that 1 = 1.