Verify that each equation is an identity.

1/(sec α - tan α) = sec α + tan 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.

1 + cot(-θ)/cot(-θ)

Verify that each equation is an identity.

(csc θ + cot θ)/(tan θ + sin θ) = cot θ csc 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.

[1 - sin²(-θ)]/[1 + cot²(-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 - sin θ

Verify that each equation is an identity.

(sin⁴ α - cos⁴ α )/(sin² α - cos² α) = 1

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 - cos θ) (csc θ + sec θ)

Verify that each equation is an identity.

(cot² t - 1)/(1 + cot² t) = 1 - 2 sin² t