Express `tan^(-1)(sqrt((1-cosx)/(1+cosx))), x lt pi`, in the simplest form.

(dy)/(dx)=(1-cos x)/(1+cosx)

Write cot^(-1) (sqrt(1+x^(2))-x) in the simplest form.

Find f'(x), if f(x)= tan^(-1) ""sqrt((1-cos2x)/(1+cos2x))

Express tan^(-1) ((3a^(2)x -x^(3))/( a^(3) -3ax^(2))) , where a gt 0, (-a)/(sqrt(3)) le x le (a)/(sqrt(3)) in the simplest form.

Solve : int(sin x)(sqrt(1+cosx) ) dx

Prove that tan^(-1) sqrt(x) =(1)/(2) cos^(-1) ((1-x)/(1+x)) , x in [0, 1]

Solve "tan"^(-1)(1-x)/(1+x) =(1)/(2) "tan"^(-1)x, x gt 0 .

Evaluate the integrals int(cosx)(1+cosx)dx