Pythagorean Identites

1+tan^2x=secx

1+cot^2x=cosx

sin^2x+cos^2x=1

These pythagorean identites are the gist of how to figure out if there are trig identities in your problem. Knowing these identities is essential to one's success in getting to the right answer.

For example in verifying identites:

1. cos^2x-sin^2x =1-2sin^2x

Start with left side using the identity sin^2x+cos^2x=1 or cos^2x= -sin^2x+1

2. cos^2x-sin^2x= (1-sin^2x)- sin^2x

3. It equals 1-2sin^2x