Verify that each equation is an identity.

(tan² α + 1)/ sec α = sec α

Perform each transformation. See Example 2.

Write cot x in terms of csc x.

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.

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

Verify that each equation is an identity.

sec⁴ x - sec² x = tan⁴ x + tan² x