6. Trigonometric Identities and More Equations

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°

In Exercises 39–46, use a half-angle formula to find the exact value of each expression. 7𝝅tan -------- 8

In Exercises 47–54, use the figures to find the exact value of each trigonometric function.θsin -------2

In Exercises 47–54, use the figures to find the exact value of each trigonometric function.θtan -------2

In Exercises 47–54, use the figures to find the exact value of each trigonometric function.αcos -------2

In Exercises 55–58, use the given information to find the exact value of each of the following:αa. sin ------24tan α = ------ , 180° < α < 270°3

In Exercises 55–58, use the given information to find the exact value of each of the following:αb. cos ------24tan α = ------ , 180° < α < 270°3

In Exercises 55–58, use the given information to find the exact value of each of the following:αc. tan ------24tan α = ------ , 180° < α < 270°3