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 each identity. csc θ - sin θ = cot θ cos θ

Verify each identity. cos² θ (1 + tan² θ) = 1

In Exercises 1–60, verify each identity. cot² t /csc t = csc t - sin t

If θ is an acute angle and sin θ = (2√7) / 7, use the identity sin²θ + cos²θ = 1 to find cos θ.

In Exercises 67–74, rewrite each expression in terms of the given function or functions. $\frac{\tan x+\cot x}{\csc x}$; $\cos x$