" (ii) "lan^(-1)(sqrt((1-cos x)/(1+cos x))),0

tan ^(-1)(sqrt((1-cos 3 x)/(1+cos x)))

(v) tan^(-1)sqrt((1+cos x)/(1-cos x))

cos^(-1)(sqrt(1+cos x)/2)

cos^(-1)(sqrt((1+cos x)/2))

Prove that: (i)tan^(-1){(sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))}=(pi)/(4)+(x)/(2)

arctan^(-1)((cos x)/(1-sin x))-cos^(-1)(sqrt((1+cos x)/(1-cos x)))=(pi)/(4),x in(0,(pi)/(2))

Simplest form of tan^(-1)((sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))), pi lt x lt (3 pi)/(2) is:

Differentiate 'tan^(^^)(-1){sqrt((1+cos x)/(1-cos x)},darr backslash0

(d)/(dx)log[sqrt((1-cos x)/(1+cos x))]=

Prove that: tan^(^^)(-1){(sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))}=pi/4-x/2, if pi