JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

{\sin ^{ - 1}}a + {\sin ^{ - 1}}b + {\sin ^{ - 1}}c = \pi ,

then the value of

a\sqrt {\left( {1 - {a^2}} \right)} + b\sqrt {\left( {1 - {b^2}} \right)} + c\sqrt {1 - {c^2})} \;

will be

View answer and explanation

Correct option: A

abc

Option A (2

abc

) is correct because the given condition

{\sin ^{ - 1}}a + {\sin ^{ - 1}}b + {\sin ^{ - 1}}c = \pi

leads to the identity

\sin 2A + \sin 2B + \sin 2C = 4 \sin A \sin B \sin C

, which simplifies to

a\sqrt {\left( {1 - {a^2}} \right)} + b\sqrt {\left( {1 - {b^2}} \right)} + c\sqrt {1 - {c^2})} = 2abc

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