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

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

Show that: sin^2 alpha + sin^2 beta + 2sinalpha sinbeta cos(alpha+beta)=sin^2 (alpha+beta)

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

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

Simplify 2sin^2beta+4cos(alpha+beta)sinalphasinbeta+cos2(alpha+beta)

Find the value of sin (alpha - beta), cos (alpha -beta) and tan (alpha - beta), given sin alpha = (8)/(17) , tan beta = (5)/(12), alpha and beta in Quadrant I.

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

Show that cos ^2 alpha + cos^2 (alpha +Beta) - 2 cos alpha cos betacos (alpha+ beta) =sin^2 beta