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)+..

Find the sum of the series sinalpha+sin(alpha+beta)+sin(alpha+2beta)+sin(alpha+3beta)+.....+sin(alpha+(n-1)beta)

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

Find the value of, cos alpha cos beta, cos alpha sin beta, -no alpha-sin beta, cos beta, 0 sin alpha cos beta, sin alpha sin beta, cos alpha] |

The expression cos^(2)(alpha+beta)+cos^(2)(alpha-beta)-cos2 alpha cos2 beta 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