Use one or more of the six sum and difference identities to solve Exercises 13–54. In Exercises 13–24, find the exact value of each expression. cos(135° + 30°)

Each expression is the right side of the formula for cos (α - β) with particular values for α and β. Write the expression as the cosine of an angle.

$\cos \frac{5\pi }{12}\cos \frac{\pi }{12}+\sin \frac{5\pi }{12}\sin \frac{\pi }{12}$

Each expression is the right side of the formula for cos (α - β) with particular values for α and β. Find the exact value of the expression.

$\cos \frac{5\pi }{12}\cos \frac{\pi }{12}+\sin \frac{5\pi }{12}\sin \frac{\pi }{12}$

In Exercises 57–64, find the exact value of the following under the given conditions:

a. cos (α + β)

sin α = 3/5, α lies in quadrant I, and sin β = 5/13, β lies in quadrant II.

In Exercises 57–64, find the exact value of the following under the given conditions:

a. cos (α + β)

tan α = ﹣3/4, α lies in quadrant II, and cos β = 1/3, β lies in quadrant I.

In Exercises 57–64, find the exact value of the following under the given conditions:

a. cos (α + β)

cos α = 8/17, α lies in quadrant IV, and sin β = -1/2, β lies in quadrant III.

In Exercises 57–64, find the exact value of the following under the given conditions:

a. cos (α + β)

tan α = 3/4, 𝝅 < α < 3𝝅/2, and cos β = 1/4, 3𝝅/2 < β < 2𝝅