" (i) "tan^(-1)(sqrt(1+x^(2))+x)quad " एंढ़त "x=cot theta" रंड "

Consider y=tan^-1((sqrt(1+x^2)+1)/x) . Put x= tan theta and show that (sqrt(1+x^2)+1)/x=tan(pi/2-theta/2) .

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

cot(tan^(-1)x+cot^(-1)x)

tan^(-1)(cot x)-tan^(-1)(cot2x)=

" In "/_\PQR, /_Q=90^(@)/_P=theta^(@)" and "/_R=phi , PR=x+2 Find (i) (sqrt(x+1))cot phi (ii) (sqrt(x^(3)+x^(2)))tan theta" (iii) "cos theta

[" 0.",int sin^(-1)sqrt((x)/(a+x))dx" is equal to "],[," 1) "(x+a)tan^(-1)sqrt((x)/(a))-sqrt(ax)+C],[" 3) "(x+a)cot^(-1)sqrt((x)/(a))-sqrt(ax)+C," 2) "(x+a)tan^(-1)sqrt((x)/(a))+sqrt(ax)+C]

int(tan(cos^(-1)x)+cot(sin^(-1)x))/(sqrt(1-x^(2)))dx=

If f(x)=(log_(cot x)tan x)(log_(tan x)cot x)^(-1)+tan^(-1)((x)/(sqrt(4-x^(2)))) then f'(0) is equal to