Write the following function in the simplest form: `tan^(-1)x/(sqrt(a^2-x^2)),|x|

Write the following functions in the simplest form: tan^(-1){x/(sqrt(a^2-x^2))}

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 function in the simplest form: tan^(-1)(1/(sqrt(x^2-1))),|x|>1

Write the following function in the simplest form: tan^(-1)((sqrt(1+x^2)-1)/x ), x!=0

Write the following functions in the simplest form: (i) sin^(-1){x/(sqrt(x^2+a^2))} (ii) cos^(-1){x/(sqrt(x^2+a^2))}

Write the following function in the simplest form: tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))

Write the following function in the simplest form: tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))

Write the following function in the simplest form: tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))

Write each of the following in the simplest form: tan^(-1){x/(a+sqrt(a^2-x^2))} where -a < x < a (ii) sin^(-1){(x+sqrt(1-x^2))/(sqrt(2))} , -1/2 < x < 1/(sqrt(2))

tan^(-1)""(x)/(sqrt(a^(2)-x^(2))),|x|lt a