Find the sum of the series `cosalpha+x cos(alpha+beta)+ x^2/(2!)cos(alpha+2beta)+…to oo`

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

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

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 series cosalpha+^nC_1 cos(alpha+beta)+^nC_2 cos (alpha+2beta)+…+cos(alpha+nbeta)

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)+….

The expression cos^2(alpha+beta)+cos^2(alpha-beta)-cos2alphacos2beta is

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

If the sides of a right angled triangle are {cos 2 alpha + cos 2 beta + 2 cos (alpha+beta)} and {sin 2 alpha+sin 2 beta + 2 sin (alpha+beta)} then the length of the hypotneuse is