Prove that `costhetacos2theta. . . cos2^(n-1)theta=(sin2^(n)theta)/(2^(n)sintheta),AAninN`.

Using induction, prove that cos theta · cos 2theta · cos 2^2 theta. ... cos 2^(n-1) theta =(sin2^n theta)/(2^n sin theta)

Prove that cos theta cos 2 theta cos 4 theta…. Cos 2 ^(n-1) theta = ( sin ( 2 ^(n) theta))/( 2 ^(n) (sin theta)) .

Prove that sintheta+sin3theta+sin5theta+.....+sin(2n-1)theta=(sin^2ntheta)/(sintheta)dot

Prove that sintheta+s in3theta+sin5theta++sin(2n-1)theta=(sin^2ntheta)/(sintheta)dot

Prove that: costhetacos(theta/2)-cos3thetacos((9theta)/2)=sin((7theta)/2)\ sin4thetadot

Statement I Pi_(r=1)^(n) (1+sec 2^(r)theta)=tan 2^(n)theta cot theta Statement II Pi_(r=1)^(n) cos (2^(r-1)theta)=(sin(2^(n)theta))/(2^(n)sin theta)

Prove that (cos theta+sin theta )^2 + (cos theta - sin theta )^2 =2

Prove that costhetacos""(theta)/(2)-cos3 thetacos""(9theta)/(2)=sin7thetasin8theta .

Prove that sin(2theta)/(1-cos2theta)=cot theta

Prove that (sintheta"cosec"thetatanthetacottheta)/(sin^(2)theta+cos^(2)theta)=1