" 4.(i) "tan^(-1)sqrt(x)

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

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

Write the following functions in the simplest form: (i) tan^(-1){x/(sqrt(a^2-x^2))},\ -a< x < a (ii) tan^(-1){sqrt((a-x)/(a+x))},\ -a< x < a

Write the following functions in the simplest form: (i) tan^(-1){x/(sqrt(a^2-x^2))},\ -a< x < a (ii) tan^(-1){sqrt((a-x)/(a+x))},\ -a< x < a

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

Differentiate the following functions with respect to x : (i) tan^(-1){sqrt(1+x^2)-x} , x in RR (ii) tan^(-1){(sqrt(1+x^2)-1)/x},\ \ x!=0

if int tan^(-1)sqrt(x)dx=u tan^(-1)sqrt(x)-sqrt(x)+c then u=

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)

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