`sin alpha + sin 2alpha + sin 4alpha + sin 5alpha=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)

( 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 ) =

Prove the following identities: (sin alpha sin 11 alpha + sin 3 alpha sin 7 alpha)/(sin alpha cos 11 alpha + sin 3 alpha cos 7 alpha)= tan 8 alpha

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

( sin 8 alpha * cos alpha - sin 6 alpha * cos 3 alpha )/(cos 2 alpha cos alpha - sin 3 alpha * sin 4alpha ) =

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

(( cos alpha - cos 3 alpha ) ( sin 8 alpha + sin 2 alpha ))/( ( sin 5 alpha - sin alpha ) ( cos 4 alpha - cos 6 alpha ))=

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

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=