The number of real solutions of `tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+x+1)=pi/2` is `z` ero b. one`` c. two d. infinite

Options

A. 0
B. 1
C. 2
D. infinite

Explanation

`tan^(1)sqrt(x(x+1)) +sin^(-1)sqrt(x^(2))+x+1)`
are defined if
`x(x+1)le0 and x^(2)+x+1le1`
`rarr x^(2)+xge0 and x^(2)+xle0`
`rarr x^(2)+x+0rarrrx=0,-1`
Thus LHS of the given equation is meaning for x =0 -1
For x=0 we have
LHS `=tan^(-1)+sin^(-1)1=(pi)/(2)=RHS`
for x=1 we have
LHS`=tan(-1) 0 + sin^(-1)1=(pi)/(2)=RHS`
Hence there are two real solutions of the given equation