Verify that each equation is an identity.

sin² α + tan² α + cos² α = sec² α

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.

tan θ cos θ

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

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

Verify that each equation is an identity.

(sec α - tan α)² = (1 - sin α)/(1 + sin α)

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