Prove the following:`sqrt(2+sqrt(2+2cos4theta))=2costheta`

Select and write the correct answer from the given alternatives in each of the following: sqrt(2+sqrt(2+2cos4theta))=

Prove the following: sqrt(frac(1-cos2theta)(1+cos2theta))=tantheta

Prove the following: sqrt(2+sqrt(+2sqrt(2+2cos8x)))=2cosx

Prove that: \ sqrt(2+sqrt(2+2cos4theta))=2costheta

Prove the following: tan^-1(sqrt(frac{1-costheta}{1+costheta})) = frac{theta}{2} , if theta lies in (-pi,pi)

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

Prove the following: (sintheta+cosectheta)^2+(costheta+sectheta)^2=Tan^2theta+cot^2theta+7

Prove the following: (frac(sintheta)(1+costheta))=tan(theta/2)

Prove the following: sin pi/8=1/2(sqrt(2-sqrt2))

Prove the following: sin^4theta+cos^4theta=1-2sin^2thetacos^2theta