JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

{\sin ^{ - 1}}x + {\sin ^{ - 1}}y + {\sin ^{ - 1}}z = \frac{{\;\;\;\;\;3\pi }}{2}\;\mathrm{and}\;f\left( 1 \right) = 2

f\left( {p + q} \right) = f\left( p \right).f\left( q \right),\forall \;p,\;q \in R,\;

then

{x^{f\left( 1 \right)}} + {y^{f\left( 2 \right)}} + {z^{f\left( 3 \right)}} - \frac{{\left( {x + y + z} \right)}}{{{x^{f\left( 1 \right)}} + {y^{f\left( 2 \right)}} + {z^{f\left( 3 \right)}}}}\;

is equal to

View answer and explanation

Correct option: C

Option A (2) is correct because given the conditions, x, y, and z must be 1, and using the functional equation, we can find f(1), f(2), and f(3), then substitute to get the result.

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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