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

Prove the following: tan pi/8=sqrt2-1

Prove the following: sin36^ °=(frac(sqrt10-2sqrt5)(4))

Prove the following: sin18^@=(frac(sqrt5-1)(4))

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

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

Prove the following: sin^-1(frac{1}{sqrt2})-3sin^-1(frac{sqrt3}{2}) = frac{-3pi}{4}

Prove the following: sqrt(frac(1+sin2x)(1-sin2x))=tan(pi/4+x)

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

Prove the following: cos(pi/4+x)+cos(pi/4-x)=sqrt2cosx