6. Trigonometric Identities and More Equations

In Exercises 57–64, find the exact value of the following under the given conditions:a. cos (α + β)3 1tan α = ﹣ ------ , α lies in quadrant II, and cos β = ------- , β lies in quadrant I.4 3

In Exercises 57–64, find the exact value of the following under the given conditions:a. cos (α + β)8 1cos α = ------ , α lies in quadrant IV, and sin β = ﹣------- , β lies in quadrant III.17 2

In Exercises 57–64, find the exact value of the following under the given conditions:a. cos (α + β)3 3𝝅 1 3𝝅 tan α = ------ , 𝝅 < α < -------- , and cos β = ------- , ---------- < β < 2𝝅.4 2 4 2

In Exercises 69–74, rewrite each expression as a simplified expression containing one term.cos (α + β) cos β + sin (α + β) sin β

Be sure that you've familiarized yourself with the first set of formulas presented in this section by working C1–C4 in the Concept and Vocabulary Check. In Exercises 1–8, use the appropriate formula to express each product as a sum or difference.sin 6x sin 2x

Be sure that you've familiarized yourself with the first set of formulas presented in this section by working C1–C4 in the Concept and Vocabulary Check. In Exercises 1–8, use the appropriate formula to express each product as a sum or difference.cos 7x cos 3x

In Exercises 14–19, use a sum or difference formula to find the exact value of each expression.cos(45° + 30°)

In Exercises 35–38, find the exact value of the following under the given conditions:b. cos(α﹣β)3 𝝅 12 𝝅 sin α = ------- , 0 < α < -------- , and sin β = --------- , --------- < β < 𝝅. 5 2 13 2

In Exercises 35–38, find the exact value of the following under the given conditions:βe. cos -------23 𝝅 12 𝝅 sin α = ------- , 0 < α < -------- , and sin β = --------- , --------- < β < 𝝅. 5 2 13 2

In Exercises 35–38, find the exact value of the following under the given conditions:b. cos(α﹣β)1 3𝝅 1 3𝝅 sin α =﹣ ------ , 𝝅 < α < ------- , and cos β =﹣------ , 𝝅 < β < ---------. 3 2 3 2

In Exercises 35–38, find the exact value of the following under the given conditions:βe. cos -------21 3𝝅 1 3𝝅 sin α =﹣ ------ , 𝝅 < α < ------- , and cos β =﹣------ , 𝝅 < β < ---------. 3 2 3 2

Use the following conditions to solve Exercises 1–4:4 𝝅sin α = ----- , ------- < α < 𝝅5 25 𝝅cos β = ------ , 0 < β < ------13 2Find the exact value of each of the following.cos (α + β)