6. Trigonometric Identities and More Equations

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. $\frac{\tan x+\cot x}{\csc x}$; $\cos x$

In Exercises 67–74, rewrite each expression in terms of the given function or functions. $\frac{\cos x}{1+\sin x}+\tan x$ ; $\cos x$

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

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. tan(7𝝅/8)

In Exercises 47–54, use the figures to find the exact value of each trigonometric function. sin(θ/2)

In Exercises 47–54, use the figures to find the exact value of each trigonometric function. tan(θ/2)

In Exercises 59–68, verify each identity. $\cot \frac{x}{2}=\frac{\sin x}{1-\cos x}$

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. sin 6x + sin 2x

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. sin 7x ﹣ sin 3x

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. cos 4x + cos 2x