JEE Advance - Mathematics (1999 - No. 37)
The number of real solutions of
$${\tan ^{ - 1}}\,\,\sqrt {x\left( {x + 1} \right)} + {\sin ^{ - 1}}\,\,\sqrt {{x^2} + x + 1} = \pi /2$$ is
$${\tan ^{ - 1}}\,\,\sqrt {x\left( {x + 1} \right)} + {\sin ^{ - 1}}\,\,\sqrt {{x^2} + x + 1} = \pi /2$$ is
zero
one
two
infinite
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