The equation `sin^-1x-cos^-1x=cos^-1(sqrt3/2)` has

Options

A. non solution
B. unique solution
C. infinite number of solution
D. None of above

Answer

B

Explanation

`sin^(-1)x- cos^(-1) x= cos ((sqrt(3))/(2))`
` sin ^(-1)x-cos^(-1)x=(pi)/(6)" ".....(i)`
`sin^(-1) x+ cos^(-1)x=(pi)/(2) " "..(ii)`
On solving Eqs. (i) and (ii) we, get
`sin^(-1)x =(pi)/(3) and cos^(-1) x=(pi)/(6)`
`x=(sqrt(3))/(2)` is the unique solution