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

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

f(alpha,beta) = cos^2(alpha)+ cos^2(alpha+beta)- 2 cosalpha cosbeta cos(alpha+beta) is

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

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

Prove that for all ninN Cosalpha+cos(alpha+beta)+cos(alpha+2beta)+ . . . +cos[alpha+(n-1)beta] = (cos[alpha+((n-1)/(2))beta]"sin"((nbeta)/(2)))/("sin"(beta)/(2))

Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+beta)=sin^2beta

By geometrical interpretation, prove that (i) sin(alpha+beta)=sin alpha cos beta+sinbeta cosalpha (ii) cos(alpha+beta)=cosalpha cosbeta -sin alpha sinbeta

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

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

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