If ${\sin ^{ - 1}}x + {\sin ^{ - 1}}\left( {1 - x} \right) = {\cos ^{ - 1}}x$, then $x$ belongs to

$\left\{ {1,{\rm{ }}0} \right\}$

$\left\{ { - 1,{\rm{ }}1} \right\}$

$\left\{ {2,{\rm{ }}0} \right\}$

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

1 of 1

Application +4 | -1

{\sin ^{ - 1}}x + {\sin ^{ - 1}}\left( {1 - x} \right) = {\cos ^{ - 1}}x

, then

x

belongs to

View answer and explanation

Correct option: C

\left\{ {0,\frac{1}{2}} \right\}

Option C (

\left\{ {0,\frac{1}{2}} \right\}

) is correct because these are the solutions obtained after simplifying the given equation and checking for validity.

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