`L e tf(n)=1+1/2+1/3++1/ndot` Then show that `f(n)=int_0^(pi/2)cot(theta/2)(1-cos^ntheta)d theta`

Find int_(0)^(pi//2)(1-cos theta)^(1//2)d theta

What is int_0^(pi//2) (d theta)/(1+ cos theta) equal to

int_(0)^(pi//2) (sin^(2)theta)/ (1+cos theta)^(2) d theta =

If 3cot theta=4 then show that (1-tan^(2)theta)/(1+tan^(2)theta)=(cos^(2)theta-sin^(2)theta)

int_(0)^( pi)(sin theta+cos theta)/(sqrt(1+sin2 theta))d theta

Show that e^(2mi theta)((i cot theta+1)/(i cot theta-1))^(m)=1

Let the be an integrable function defined on [0,a] if I_(1)=int_(pi//2)^(pi//2) cos theta f(sin theta cos ^(2) theta)d theta and I_(2)=int_(0)^(pi//2)sin 2 theta f(sin theta cos ^(2) theta)d theta then