Prove that `(1- sin 2x)/(1+ sin 2x) = tan^(2) .((pi)/(4)-x)`

Prove that : (1-sin2x)/(1+sin2x)= tan^2 (pi/4-x) .

Prove that (cos x)/((1- sin x)) = tan .((pi)/(4) + (x)/(2))

i) Prove that: (1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A) ii) If costheta=1/2(x+1/x) , then prove that: cos2theta=1/2(x^(2)+1/x^(2)) and cos3theta=1/2(x^(3)+1/x^(3))

i) Prove that: (1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A) ii) If costheta=1/2(x+1/x) , then prove that: cos2theta=1/2(x^(2)+1/x^(2)) and cos3theta=1/2(x^(3)+1/x^(3))

Prove that : sin^-1 x + sin^-1 2x = pi/3

sqrt((1+sin x)/(1-sin x))=tan((pi)/(4)+(x)/(2))

Prove that, tan^(-1)((3 sin 2x)/(5+3 cos 2x))+tan^(-1)((1)/(4) tan x)=x .

Prove that : cos^(-1) x = 2 cos^(-1) sqrt((1+x)/(2)) (ii) Prove that : tan^(-1)((cosx + sin x)/(cosx - sin x)) = (pi)/(4)+ x

Prove that (1+ sin 2x - cos 2x)/(1+ sin 2x + cos 2x) =tan x

Prove that (sin 4x + sin 2x)/(cos 4x + cos 2x) = tan 3x .