Verifying Identities Worksheet with Answer Key

What's on the worksheet

1. Verify each identity by working on one side only, naming the identity used at each step.
   \sec x\csc x\cos^2 x = \cot x(1 - \sin^2 x)(1 + \cot^2 x) = \cot^2 x\sec^2 x\cot^2 x - \cot^2 x = 1\dfrac{\tan^2 x}{\sec x} = \sec x - \cos x
2. Verify each identity and state its common domain.
   \dfrac{1}{\sec x - \cos x} = \cot x\csc x\dfrac{\sin x}{\csc x + \cot x} = 1 - \cos x
3. Decide whether each equation is an identity.
   \dfrac{\cot x - \tan x}{\sin x\cos x} = \csc^2 x - \sec^2 x\cos^4 x - \sin^4 x = 1
5. Verify x - x + 1 x + x - 1 = x + 1 x and state the common domain.
6. Elena claims that x + x = √(1 + 2 x x) for every x.