Find the sum of the series `cos^3alpha + cos^3 2alpha +......` to n terms

Find the sum of the series cos^(3)alpha+cos^(3)2 alpha+...... to n terms

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

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 cosalpha+x cos(alpha+beta)+ x^2/(2!)cos(alpha+2beta)+…to oo

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

Sum the series : (1+cos alpha) +(1+ cos2alpha) +(1+ cos3alpha) +..... to n terms.

If a_(1),alpha_(2)...,alpha_(n) are in A.P.with common difference d,then the sum of the series,sin d[cos ec alpha_(1)cos ec alpha_(2)+cos ec alpha_(2)cos ec alpha_(3)+...+...+cos ec alpha_(n-1)cos ec alpha_(n) is:

Sum the series: sin alpha - sin 2alpha + sin 3alpha - sin 4alpha + ... to n terms.

Express cos 6 alpha in terms of cos 3 alpha .

Find the sum to n terms of the following series: cos alpha + cos (pi - alpha) + cos (2pi + alpha) + .......(0 < alpha < (pi)/2) .