Question

Use a power-reducing formula to rewrite the given expression in terms of the first power of the cosine:
tan^2(8x)

Answer 1

tan²(8x) = sin²(8x) / cos²(8x)

… = (1 - cos²(8x)) / cos²(8x)

… = 1 / cos²(8x) - 1

… = 2 / (1 + cos(16x)) - 1

where the last equality follows from the half-angle identity for cosine,

cos²(x) = (1 + cos(2x)) / 2