Prove that: `(sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27 x)=(1/2)(tan27 x-tanx)`

Number of solutions (s) of the equation (sin x)/(cos 3x) +(sin 3x)/(cos 9x)+(sin 9x)/(cos 27 x)=0 in the interval (0, pi/4) is __________.

Number of solution(s) of the equation (sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27x)=0 in the interval (0,pi/4) is____________

prove that [2(sin^3 x - cos^3 x )/(sinx -cosx)]-sin2x=2

Prove that (sin4x+sin2x)/(cos4x+cos2x)=tan3x

Prove that sinx +sin2x +sin3x =sin2x (1+2cosx) .

Prove that (sin 5x -2 sin 3x + sin x)/(cos 5x - cos x)= tan x

Prove that (cos3x)/(sin2xsin4x)+(cos5x)/(sin4xsin6x)+(cos7x)/(sin6xsin8x)+(cos9x)/(sin8xsin10 x) = 1/2(cos e cx)[cos e c2x-cos e c10x]

Prove that sec x-cos x=tan x sin x

Prove that sqrt(sin^4x+4cos^2x)-sqrt(cos^4x+4sin^2x)=cos2xdot

Prove that (sinx+sin3x+sin5x+sin7x)/(cosx+cos3x+cos5x+cos7x)=tan4x