Verify that each equation is an identity.

(sin² θ)/cos θ = sec θ - cos θ

Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.

csc θ cos θ tan θ

Verify that each equation is an identity.

sec⁴ x - sec² x = tan⁴ x + tan² x

Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.

sin θ sec θ

Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.

cot² θ(1 + tan² θ)

For each expression in Column I, choose the expression from Column II that completes an identity.

6. sec² x = ____

II

A. sin ^2 x/cos ^2 x

B.1/(sec ^2 x)

C. sin (-x)

D. csc ^2 x-cot ^2 x + sin ^2 x

E. tan x

Verify that each equation is an identity.

[(sec θ - tan θ)² + 1]/(sec θ csc θ - tan θ csc θ) = 2 tan θ

Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.

(sec θ - 1) (sec θ + 1)