The value of ` I(n) =int_0^pi(sin ^2n theta)/(sin^2theta) d theta ` is `(AA n in N)`

If U_(n)=int_(0)^(pi)(1-cosnx)/(1-cosx)dx where n is positive integer of zero, then The value of int_(0)^(pi//2)(sin^(2)n theta)/(sin^(2) theta) d theta is

If I_(n)=int_(0)^(2 pi)(cos(n theta))/(cos theta)d(theta), where n in N then.

If f (n)= 1/pi int _(0) ^(pi//2) (sin ^(2) (n theta) d theta)/(sin ^(2) theta), n in N, then evulate (f (15)+ f (3))/( f (12) -f (10)).

If f (n)= 1/pi int _(0) ^(pi//2) (sin ^(2) (n theta) d theta)/(sin ^(2) theta), n in N, then evulate (f (15)+ f (3))/( f (12) -f (10)).

The value of (1+cos theta+i sin theta)^(n)+(1+cos theta-i sin theta)^n=

The value of (1+cos theta+i sin theta)^(n)+(1+cos theta-i sin theta)^(n)=

cot theta=sin 2 theta,(theta ne n pi), if theta

cot theta=sin 2 theta(theta neq n pi, n in z), if theta=

Prove that , sin theta + sin 2theta + ……+ sin n theta = ( (sin( n theta/(2)) sin ((n+1)/(2))theta))/(sin theta/2) , for all n in N .