Prove that `cos^(3)thetasin3theta+sin^(3)thetacos3theta=(3)/(4)"sin"4theta`.

Prove that sintheta+sin3theta+sin5theta+sin7theta=4costhetacos2thetasin4theta

Solve 7cos^(2)theta+3sin^(2)theta=4 .

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

The value of theta lying between theta = 0 and theta = pi//2 and satisfying the equation |(1+sin^(2)theta,cos^(2)theta,4sin4theta),(sin^(2)theta,1+cos^(2)theta,4sin4theta),(sin^(2)theta,cos^(2)theta,1+4sin4theta)|=0 are a) 3pi//24 b) 5pi//24 c) 11pi//24 d) pi//24

Prove that (cos2theta)/(1+sin2theta)=tan(pi//4-theta)

Evaluate |[cos theta, -sin theta], [sin theta, cos theta]|

Consider the trigonometric expression sin(2A)/(1-cos 2A) amd sin(2A)/(1+cos 2A) .(iii)Prove that (1-cos theta)/sin theta=tan (theta/2)=(sin theta)/(1+cos theta) .

The product of matrices A = [(cos^(2) theta, cos theta sin theta),(cos theta sin theta , sin^(2) theta)] and sin B = [(cos^(2)phi, cos phi sin phi),(cos phi sin phi, sin^(2) phi)] is a null matrix if theta - phi =

Prove that (cos(90^(@)+theta)sec(-theta)tan(180^(@)-theta))/(sec(360^(@)-theta)sin(180^(@)+theta)cot(90^(@)-theta))=-1 .