`sinalpha+sin2alpha+sin4alpha+sin5alpha`=`4cos(alpha/2)cos(3alpha/2)sin3alpha`

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

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

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

(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

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

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

( sin alpha sin 3alpha + sin 3alpha sin 7 alpha + sin 5 alpha sin 15 alpha )/( sin alpha cos 3 alpha + sin 3alpha cos 7 alpha + sin 5 alpha cos 15 alpha ) =

(sin 5 alpha-sin3alpha)/(cos 5 alpha+2 cos 4 alpha+cos 3alpha)=