`tan^(-1)((sqrt(x))/(1+20x))`

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

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

Prove that tan^(-1) ((1-sqrt(x))/(1+sqrt(x))) = pi/4 - tan^(-1) sqrt(x) , "where" x gt 0

Prove that: i) tan^(-1)(sqrt(x)+sqrt(y))/(1-sqrt(xy))=tan^(-1)sqrt(x)+tan^(-1)sqrt(y) ii) tan^(-1)(x+sqrt(x))/(1-x^(3//2))=tan^(-1)x+tan^(-1)sqrt(x) iii) tan^(-1)(sinx)/(1+cosx)=x/2

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

Differentiate tan^(-1)x/(1+sqrt((1-x^2))) +{2tan^(-1)sqrt(((1-x)/(1+x)))}sinwdotrdottdotxdot

Differentiate tan^(-1)(x/(1+sqrt((1-x^2)))) +{2tan^(-1)sqrt(((1-x)/(1+x)))}sinwdotrdottdotxdot

tan^(-1)((x)/(sqrt(1-x)))