Verify that each equation is an identity.

sin² β (1 + cot² β) = 1

Perform each transformation. See Example 2.

Write sec x in terms of sin x.

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

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

Verify that each equation is an identity.

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