If ${\sin ^{ - 1}}x - {\cos ^{ - 1}}x = \frac{\pi }{6},$ then $x$ is

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

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Application +4 | -1

{\sin ^{ - 1}}x - {\cos ^{ - 1}}x = \frac{\pi }{6},

then

x

View answer and explanation

Correct option: B

\frac{{\sqrt 3 }}{2}

Option B is correct because solving the equation

{\sin ^{ - 1}}x - {\cos ^{ - 1}}x = \frac{\pi }{6}

using trigonometric identities leads to

x = \frac{{\sqrt 3 }}{2}

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