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

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)+..

If cos(alpha+beta)=0 then sin(alpha+2beta)=

Find the sum to n terms o the series cos^2 alpha+cos^2(alpha+beta)+cos^2(alpha+2beta)+..

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

Prove that: cos2alpha\ cos2beta+sin^2(alpha-beta)-sin^2(alpha+beta)=cos2(alpha+beta) .

If the lines x(sinalpha+sinbeta)-ysin(alpha-beta)=3 and x(cosalpha+cosbeta)+ycos(alpha-beta)=5 are perpendicular then sin2alpha+sin2beta is equal to:

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

If 5 sinalpha=3"sin"(alpha+2beta)!=0, then tan(alpha+beta) is equal to

The value of the determinant Delta = |(sin 2 alpha,sin (alpha + beta),sin (alpha + gamma)),(sin (beta + gamma),sin 2 beta,sin (gamma + beta)),((sin gamma + alpha),sin (gamma + beta),sin 2 gamma)| , is