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^

1.	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))`
Answer» `tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2)))` `tan^(-1)((3a^(2)a tan theta-a^(3)tan^(3)theta)/(a^(3)-3aa^(2)tan^(2)theta))` `=tan^(-1)((3 tan theta-tan^(3)theta)/(1-3 tan^(2)theta))" " Let x = a tan theta implies (x)/(a)=tan thetaimplies theta = tan^(-1)""((x)/(a))` `=tan^(-1)(tan 3 theta)3 theta` `3 tan^(-1)""(x)/(a)`

If `sin ^(-1) .(2a)/(1+a^(2))+ coses^(2) (cot ^(-1) 3) y =?`A. `(a+b)/(1-ab)`B. `(a+b)/(1+ab)`C. `(a-b)/(1+ab)`D. None of these
Prove that:`tan^(-1)1/5+tan^(-1)1/7+tan^(-1)1/3+tan^(-1)1/8=pi/4`
`If"sin"{cot^(-1)(x+1)}="cos"(tan^(-1)x),`then find `xdot`A. `sqrt((x^(2)+2)/(x^(2)+1))`B. `(x)/sqrt(x^(2)+1)`C. `(x)/sqrt(x^(2)+2)`D. `sqrt((x^(2) +1)/(x^(2) + 2))`
If `(tan^(-1)x)^2+(cot^(-1)x)^2=(5pi^2)/8,`then find `xdot`A. 1B. -1C. `(1)/sqrt(3)`D. `-(1)/sqrt(3)`
The Principal value of `os^(-1) (sqrt(3)/(2))` is :A. `(pi)/(8)`B. `(pi)/(6)`C. `(pi)/(3)`D. None of these
If `sin(sin^(-1)1/5+cos^(-1)x)=1,`then find the value of `xdot`
`sec^(2) (tan^(-1) 4) + cosec^(2) (cot ^(-1) 3) =?`A. 30B. 29C. 27D. 25
`tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3))`is equal to(A) `pi` (B) `-pi/2` (C) 0 (D) `2sqrt(3)`A. `pi`B. `-(pi)/(2)`C. `0`D. `2sqrt(3)`
Prove that:`sin^(-1)8/(17)+sin^(-1)3/5=tan^(-1)(77)/(36)`
Find the value of: `tan1/2[sin^(-1)(2x)/(1+x^2)+cos^(-1)(1-y^2)/(1+y^2)],|x|0`and `x y" "