6. Trigonometric Identities and More Equations

Verify that each equation is an identity.

sin θ + cos θ = sin θ/(1 - cot θ) + cos θ/(1 - tan θ)

Let csc x = -3. Find all possible values of (sin x + cos x)/sec x.

Use identities to write each expression in terms of sin θ and cos θ, and then simplify so that no quotients appear and all functions are of θ only.

cot(-θ)/sec(-θ)

Verify that each equation is an identity.

(1 + sin x + cos x)² = 2(1 + sin x) (1 + cos x)

Verify that each equation is an identity.

(sec α + csc α) (cos α - sin α) = cot α - tan α

Verify that each equation is an identity.

(1 - cos θ)/(1 + cos θ) = 2 csc² θ - 2 csc θ cot θ - 1

Verify that each equation is an identity.

sin² x(1 + cot x) + cos² x(1 - tan x) + cot² x = csc² x

Verify that each equation is an identity.

sin³ θ + cos³ θ = (cos θ + sin θ) (1 - cos θ sin θ)