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

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

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

Prove the following: tan^-1 1+tan^-1 2+tan^-1 3 = pi

Prove the following: tan[pi/4+1/2cos^(-1)(a/b)]+tan[pi/4-1/2cos^(-1)(a/b)]=(2b)/a

Prove the following: tan^-1[sqrt(frac{1-cosx}{1+cosx})] = frac{x}{2}

Prove the following: sqrt2cos(pi/4-A)=cosA+sinA

Prove the following: tan(pi/4-theta)=(frac(1-tantheta)(1+tantheta))

Prove the following: (tan^3 theta - 1)/(tan theta - 1) = sec^2 theta + tan theta

Prove the following : (tan^3 theta -1)/( tan theta-1) = sec^2 theta + tan theta

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