`sinalpha-sin2alpha+sin3alpha=4cos\ (3alpha)/2cosalphasin\ alpha/2`

if A,=[[cos alpha,sin alpha-sin alpha,cos alphasin alpha,cos alphacos2 alpha,sin2 alpha-sin2 alpha,cos2 alpha]]

Prove that (sin alpha+sin2 alpha+sin3alpha+sin4alpha)/(cos alpha+cos 2 alpha+cos 3 alpha+cos4 alpha)=tan((5 alpha)/2)

sin alpha+sin2 alpha+sin4 alpha+sin5 alpha=4cos((alpha)/(2))cos(3(alpha)/(2))sin3 alpha

sin alpha+sin2 alpha+sin4 alpha+sin5 alpha=4cos((alpha)/(2))cos(3(alpha)/(2))sin3 alpha

(sin alpha*sin3 alpha+sin3 alpha*sin7 alpha+sin5 alpha*sin15 alpha)/(sin alpha*cos3 alpha+sin3 alpha cos7 alpha+sin5 alpha*cos15 alpha)=

prove that (sin alpha+sin3 alpha+sin5 alpha)/(cos alpha+cos3 alpha+cos5 alpha)=tan3 alpha

If alpha is any real nubmer then: (sin^4alpha+sin^2alpha.cos^2alpha+cos^2alpha)/(cos^4alpha+sin^2alpha.cos^2alpha+sin^2alpha)=.... (a) 1 (b)2 (c) 3 (d) none of these

Prove the identity,cos((3 pi)/(2)+4 alpha)+sin(3 pi-8 alpha)-sin(4 pi-12 alpha)=4cos2 alpha cos4 alpha sin6 alpha

Let f_n(a)=(sinalpha+sin3alpha+sin5alpha+...+sin(2n-1)alpha)/(cosalpha+cos3alpha+cos5alpha+...+cos(2n-1)alpha) Then, the value of f_4(pi/32) is equal to

Let f_n(a)=(sinalpha+sin3alpha+sin5alpha+...+sin(2n-1)alpha)/(cosalpha+cos3alpha+cos5alpha+...+cos(2n-1)alpha) Then, the value of f_4(pi/32) is equal to