`sinfrac{1}{2}(n+1)theta-sinfrac{1}{2}(n-1)theta=sintheta`

sin^2 n theta- sin^2 (n-1)theta= sin^2 theta where n is constant and n != 0,1

Prove that sin^2 theta+sin^2 2theta+sin^2 3theta+....+sin^2 n theta=n/2-(sin n theta cos(n+1)theta)/(2sin theta)

Solve it sin((k+1)/2)theta-sin((k-1)/2)theta=sintheta

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

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)

Simplify: (1+tan^(2)theta)(1-sintheta)(1+sintheta)

Prove that: (i) (costheta)/(1-sintheta)=(1+sintheta)/(costheta) (ii) (1+costheta-sin^(2)theta)/(sintheta+sinthetacostheta)=cottheta (iii) 1+(tan^(2)theta)/(1+sectheta)=sectheta

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

Show : (1+tan^2theta)(1+sintheta)(1-sintheta) = 1