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

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

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

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

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

Prove,by induction,that sin alpha+cos(alpha+beta)-sin(alpha+2 beta)-cos(alpha+3 beta)+sin(alpha+4 beta)+... to n terms

2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(alpha+beta)=

Sum the series tan alpha tan (alpha+beta)+tan(alpha+beta)+tan(alpha+2beta)+tan(alpha+2beta)tan(alpha+3beta)+… to n terms

Sum the series tan alpha tan (alpha+beta)+tan(alpha+beta)+tan(alpha+2beta)+tan(alpha+2beta)tan(alpha+3beta)+… to n terms

If sinalpha+sin beta=a and cos alpha+cos beta=b,then sin(alpha+beta)=