6. Trigonometric Identities and More Equations

In Exercises 1–60, verify each identity.csc θ - sin θ = cot θ cos θ

In Exercises 1–60, verify each identity.cos θ sec θ ----------------- = tan θcot θ

In Exercises 1–60, verify each identity.cos² θ (1 + tan² θ) = 1

In Exercises 1–60, verify each identity.cot² t------------ = csc t - sin tcsc 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.tan x + cot x---------------------- ; cos xcsc x

In Exercises 67–74, rewrite each expression in terms of the given function or functions.cos x---------------- + tan x ; cos x1 + sin x

In Exercises 67–74, rewrite each expression in terms of the given function or functions.1 cos x------------------ ﹣ ------------------- ; csc x1 - cos x 1 + cos x

In Exercises 67–74, rewrite each expression in terms of the given function or functions.(sec x + csc x) (sin x + cos x) - 2 - cot x; tan x

In Exercises 35–38, use the power-reducing formulas to rewrite each expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.6 sin⁴ x

In Exercises 35–38, use the power-reducing formulas to rewrite each expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.sin² x cos² x

In Exercises 39–46, use a half-angle formula to find the exact value of each expression.cos 22.5°

In Exercises 39–46, use a half-angle formula to find the exact value of each expression.sin 105°