a) Express 4(cosec^2(2x)) - (cosec^2(x)) in terms of sin(x) and cos (x) and hence b) show that 4(cosec^2(2x)) - (cosec^2(x)) = sec^2(x)

A) 4(cosec²(2x)) - (cosec²(x)) = 4/(sin²(2x)) - 1/(sin²(x)) = 4/[(2 sin(x) cos(x))²] - 1/(sin²(x)) B) 4/[(2 sin(x) cos(x))²] - 1/(sin²(x)) = 4/(4 sin²(x) cos²(x)) - 1/(sin²(x)) = 1/(sin²(x) cos²(x)) - cos²(x)/[sin²(x)cos²(x)] = {Using 1 - cos²(x) = sin²(x)} = sin²(x)/(sin²(x)cos²(x)) = 1/(cos²(x)) = sec²(x)