" (iv) "2cos2 theta=1+sin theta

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

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

Prove the following identity : cos^4 theta- sin^4 theta= cos^2 theta-sin^2 theta= 2 cos^2 theta-1=1-2 sin^2 theta .

Solve the following trigonometric equation : 2 cos^2 theta- 5 sin theta+1=0 .

Prove that : sin^8 theta- cos^8 theta= (sin^2 theta- cos^2 theta)(1-2 sin^2 theta cos^2 theta) .

prove : sin^8θ-cos^8θ = (sin^2 theta - cos^2 theta) (1- 2 sin^2 theta cos^2 theta)

Prove that: (1-sin theta + cos theta)^(2) = 2(1+ cos theta) (1-sin theta) .

Prove that (1-sin theta+cos theta)^(2)=2(1+cos theta)(1-sin theta)

Prove that, cot ( theta + 15^(@))- tan(theta - 15^(@))=(4 cos 2 theta)/(1+2 sin 2 theta)