The number of real roots of the equation ${\tan ^{ - 1}}\sqrt {x\left( {x + 1} \right)} {\rm{ }} + {\rm{ }}{\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = \frac{\pi }{4}$ is

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Analyzing +4 | -1

The number of real roots of the equation

{\tan ^{ - 1}}\sqrt {x\left( {x + 1} \right)} \mathrm{ } + \mathrm{ }{\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = \frac{\pi }{4}

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Correct option: D

Option D (0) is correct because the given equation has no real roots as the domain restrictions lead to a contradiction.

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