" 17."tan^(-1)[sqrt((1+cos x)/(1-cos x))]=(pi)/(2)-(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)

If x epsilon(7pi,8pi) , then "tan"^(-1)sqrt((1-"cos" x)/(1+"cos" x))=

tan ^(-1) ""{(sqrt(1+cos x)+sqrt(1-cos x)}/{sqrt(1+cosx)-sqrt(1-cos x)}}=(pi)/(4)+(x)/(2) , 0 lt x lt (pi)/(2)

prove that tan^(-1)((cos x)/(1-sin x))-cot^(-1)((sqrt(1+cos x))/(sqrt(1-cos x)))=(pi)/(4),x varepsilon(0,(pi)/(2))

tan^(-1)(sqrt((a-x)/(a+x)))=(1)/(2)cos^(-1)((x)/(a))

If x in ((pi)/(6), (pi)/(3)) " then " int tan^(-1) sqrt((1 - cos 2x)/(1 + cos 2 x)) dx =

Solve : tan^(-1)(sqrt((1-cos x)/(1+cos x))), x lt pi

convert in the simplest form: tan^(-1)(sqrt((1-cos x)/(1+cos x))),x

If pi/2

Prove that cos^(-1)((sqrt(1+x)+sqrt(1-x))/(2))=(pi)/(4)-(1)/(2)cos^(-1)x