JEE Main 2022 · 30 Jun · Shift 1 · Mathematics Q10

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MathematicsSingle correct+4 / -1Question 10 of 90

Let m and M respectively be the minimum and the maximum values of $f(x)=\sin^{-1}2x+\sin2x+\cos^{-1}2x+\cos2x$ , $x\in\left[0,\dfrac\pi8\right]$ . Then $m+M$ is equal to :

1+\sqrt2+\pi

\left(1+\sqrt2\right)\pi

\pi+\sqrt2

1+\pi

Answer and worked solution

Official answer: A

Inverse terms add to $\frac\pi2$ (here $2x\le1$ ). $\sin2x+\cos2x$ runs from 1 to $\sqrt2$ on $[0,\frac\pi4]$ .

$m+M$ $=\pi+1+\sqrt2$ .

(A)

Topics:Inverse trigonometric functions Trigonometric ratios and identities

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JEE Main 2022 · 30 Jun · Shift 1, Mathematics question 10