" (i) "tan^(-1)sqrt(x)" (ii) "tan^(-1)(2x+1)

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

Differentiate each of the following w.r.t. x: (i) tan^(-1)(sqrt(1+x^(2))+x)" "(ii)tan^(-1)(sqrt(1+x^(2))-x)

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

If 3tan^(-1)(2-sqrt(3))-tan^(-1)(x)=tan^(-1)((1)/(3)) then x=

Prove that tan^(-1)((sqrt(1+x^2)-1)/x)=1/2 tan^(-1)x .

Let |{:(tan^(-1)x, tan^(-1)2x, tan^(-1)3x), (tan^(-1)3x, tan^(-1)x, tan^(-1)2x), (tan^(-1)2x, tan^(-1)3x, tan^(-1)x):}|=0 , then the number of values of x satisfying the equation is

tan^(-1)(x+sqrt(1+x^(2)))=

int tan^(-1) sqrt x dx=.............a)x tan^(-1) sqrt x - sqrt x + tan^(-1) sqrt x + c b)x tan^(-1) sqrt x + sqrt x - tan^(-1) sqrt x + c c)- x tan^(-1) sqrt x - sqrt x + tan^(-1) sqrt x + c d)x tan^(-1) sqrt x + sqrt x + tan^(-1) sqrt x + c

If 3 tan ^(-1)((1)/(2+sqrt(3)))-tan ^(-1) (1)/(x)=tan ^(-1) (1)/(3) then x=