" 11."cos n theta=cos(n-2)theta+sin theta

cos m theta=sin n theta then theta=

If ((1 + cos theta + i sin theta ) /(i+ sin theta + i cos theta ))= cos ntheta + i sin n theta then n is equal to :

Prove that sum_(r=1)^(n)((1)/(cos theta+cos(2r+1)theta))=(sin n theta)/(2sin theta*cos theta*cos(n+1)theta),(wherenin N)

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)

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

If ((1+cos theta+i sin theta)/(sin theta+i+i cos theta))^(4)=cos n theta+i sin n theta , then n=

cos m theta-sin n theta=0

If A = [(cos theta, sin theta),(-sin theta, cos theta)] then show that for all the positive integers n, A^(n) = [(cos n theta,sin n theta),(-sin n theta,cos n theta)] .

If A=[cos theta i sin theta i sin theta cos theta], then prove by principle of mathematical induction that A^(n)=[cos n theta i sin n theta i sin n theta cos n theta] for all n in N.

Find the general value of theta which satisfies the equation (cos theta+i sin theta)(cos2 theta+i sin2 theta)......(cos n theta+i sin n theta)=1