Question

Using a double-angle or half-angle formula to simplify the given expressions.

(a) If cos² (38°) - sin² (38°) = cos(A°), then A=. Degrees

(b) If cos² (8x) - sin² (8x) = cos(B), then B=.

Answer 1

(a) Using the identity cos²θ - sin²θ = cos(2θ), we can simplify the expression as follows:cos²(38°) - sin²(38°) = cos(2×38°)= cos(76°)Therefore, A = 76°.

(b) Using the identity cos²θ - sin²θ = cos(2θ), we can simplify the expression as follows:cos²(8x) - sin²(8x) = cos(2×8x)= cos(16x)

Therefore, B = cos(16x).