(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).