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)
