`tan^(- 1)(1/(sqrt(3))tanx/2)=1/2cos^(- 1)((1+2cosx)/(2+cosx))`

Show that tan^(-1)(1/sqrt3tanx/2)=1/2 cos^(-1)(1+2cosx)/(2+cosx) .

int1/(7+5cosx)\ dx= 1/(sqrt(6))tan^(-1)(1/(sqrt(6))tanx/2)+C (b) 1/(sqrt(3))tan^(-1)(1/(sqrt(3))tanx/2)+C (c) 1/4tan^(-1)(tanx/2)+C (d) 1/7tan^(-1)(tanx/2)+C

2Tan^(-1)(cosx)=

Prove that : tan^(-1)((cosx)/(1-sinx))-cot^(-1)(sqrt((1+cosx)/(1-cosx)))=(pi)/(4), x in (0, pi//2) .

2tan^(-1)(cosx)=tan^(-1)(2cosecx)

Prove that : (1)/(2) cos^(-1) ((1+ 2 cos x)/( 2+cosx) ) = tan^(-1) ((1)/(sqrt(3)) "tan" (x)/(2))

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

tan^(-1)(sqrt((1-cosx)/(1+cosx))),0ltxltpi

The derivative of the function, f(x)=cos^(-1){(1)/(sqrt(13))(2cosx-3sinx)}+sin^(-1){(1)/(sqrt(13))(2cosx+3sinx)}w.r.tsqrt(1+x^(2)) is