JEE MATHEMATICS MCQ: MAXIMA & MINIMA

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Application +4 | -1

Greatest and least value of

\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2

are respectively

View answer and explanation

Correct option: D

\frac{5 \pi^2}{4}

and

\frac{\pi^2}{8}

Option D (

\frac{5 \pi^2}{4}

and

\frac{\pi^2}{8}

) is correct because by using the identity

(\sin^{-1} x)^2 + (\cos^{-1} x)^2 = (\sin^{-1} x + \cos^{-1} x)^2 - 2 \sin^{-1} x \cos^{-1} x

and completing the square, we can find the maximum and minimum values.

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