`cot{tan^(- 1)x+tan^(- 1)(1/x)}+cos^(- 1)(1-2x^2)+cos^(- 1)(2x^2-1)=pi, x gt0`

If tan^(- 1)((2x)/(x^2-1))+cos^(- 1){(x^2-1)/(x^2+1)}=(2pi)/3 then x=

Solve the following equations : tan^(-1). (2x)/(1-x^(2)) +cos^(-1). (1-x^(2))/(2x) = pi/3 , x gt 0

tan ^(-1)((1)/(2) sec x) + cot^(-1)(2cos x) =(pi)/(3)

tan^(-1)((2x)/(1-x^2))+cot^(-1)((1-x^2)/(2x))=pi/3

sin^-1(-x) = -sin^-1(x); cos^-1(-x) = pi - cos^-1(x); tan^-1(-x) = -tan^-1(x); cot^-1(-x) = pi - cot^-1(x); sec^-1(-x) = pi - sec^-1(x); cosec^-1(-x) = -cosec^-1(X)

Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2)) cos [tan^(-1) (cot^(-1)x)}]=sqrt((x^2+1)/(x^2+2))

2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1}, is equal to (2x)/(1-x^2) t(2tan^(-1)x) tan(cot^(-1)(-x)-cot^(-1)(x)) "tan"(2cot^(-1)x)

2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1}, is equal to (2x)/(1-x^2) t(2tan^(-1)x) tan(cot^(-1)(-x)-cot^(-1)(x)) "tan"(2cot^(-1)x)

The solution set of inequality ( cot^(-1) x) (tan^(-1) x) + (2 - pi/2) cot^(-1) x - 3 tan^(-1) x - 3 ( 2 - pi/2) gt 0 , is

The solution set of inequality ( cot^(-1) x) (tan^(-1) x) + (2 - pi/2) cot^(-1) x - 3 tan^(-1) x - 3 ( 2 - pi/2) gt 0 , is