Exhaustive set of values of parameter 'a' so that `sin^(-1)x-tan^(-1)x=a` has a solution is

Options

A. `[-pi//6,pi//6]`
B. `[-pi//4,pi//4]`
C. `(-pi//2,pi//2)`
D. none of these

Explanation

Let f(x)=`sin^(-1)-tan^(-1)x`
clearly f(x) id defined for all `x in [-2,1]`
Also
`f(x)=(1)sqrt(1-x^(1))-(1)/(1+x^(2))gt0` for all `x in (-1,1)`
`rarr` f(x) id incresasing onn (-1,1)
`rarr f(-1)lef(x)lef(1)`
`rarr -(pi)/(4)leale(pi)/(4)rarrain[-(pi)/(4),(pi)/(4)]`