Sum the infinite series :`sinalpha+x sin (alpha+beta)+ x^2/(2!)sin(alpha+2beta)+x^3/(3!) sin (alpha+3beta)+..`

Sum of n terms of the series sinalpha-sin(alpha+beta)+sin(alpha+2beta)-sin(alpha+3beta)+….

Sum of n terms of the series sinalpha-sin(alpha+beta)+sin(alpha+2beta)-sin(alpha+3beta)+….

Sum of n terms of the series sinalpha-sin(alpha+beta)+sin(alpha+2beta)-sin(alpha+3beta)+….

if tan alpha=2tan beta show that (sin(alpha+beta))/(sin(alpha-beta))=3

Find the sum of the series sin^2alpha+sin^2(alpha+beta)+sin^2(alpha+2beta)…+sin^2(alpha +(n-1) beta)

Find the sum of the series sin^2alpha+sin^2(alpha+beta)+sin^2(alpha+2beta)…+sin^2(alpha +(n-1) beta)

sin ^ (2) alpha + sin ^ (2) (alpha-beta) -2sin alpha cos beta sin (alpha-beta) = sin ^ (2)

Find the sum of the series sinalpha+sin(alpha+beta)+sin(alpha+2beta)+sin(alpha+3beta)+.....+sin(alpha+(n-1)beta)

(sinalpha cos beta+cos alpha sin beta)^2+(cos alpha cos beta-sin alpha sin beta)^2=1