Apply the formula for cos (A − B) to the identity sin θ = cos (π/2 − θ) to obtain the addition formula for sin (A + B).

A triangle has side c = 2 and angles A = π/4 and B = π/3. Find the length a of the side opposite A.

Using the Addition Formulas

Use the addition formulas to derive the identities in Exercises 31–36.

cos (x − π/2) = sin x

Using the Addition Formulas

Use the addition formulas to derive the identities in Exercises 31–36.

sin (A − B) = sin A cos B − cos A sin B

In Exercises 39–42, express the given quantity in terms of sin x and cos x.

cos (3π/2 + x)

What happens if you take B = 2π in the addition formulas? Do the results agree with something you already know?

Evaluate cos (11π/12) as cos (π/4 + 2π/3).