Review 5.2 Verifying Trigonometric Identities

In 5.2, the purpose is to verify trigonometric identities. In order to verify trigonometric identities, fundamental identities and the rules of algebra are important to be memorized. There are 4 

rules for verifying trigonometric identities:
1. Work with only one side the equation.
2. Factor an expression, add fractions, square binomials, or create a monomaniacal denominator.
3. Look for opportunities to use the fundamental identities .
4. Convert all terms to sines and cosines if the preceding guidelines do not help.


Example#1: 
2sec^2x - 2sec^2xsin^2x - sin^2x - cos^2x
=2sec^2x (1-sin^2x)-sin^2x-cos^2x Factor
=2sec^2x(cos^2x)-sin^x-cos^2x Pythagorean identities
=2(1/cos^2x)(cos^2x)-sin^x-cos^2x Reciprocal identities
=2-sin^2x-(1-sin^2x) Pythagorean identities
=2-sin^2x-1+sin^x Simplify