Question:medium

Considering only the principal values of the inverse trigonometric functions, evaluate: \[ \cot^{-1}(\cot(-11)) +10\sin\left(2\cos^{-1}\left(\frac1{\sqrt2}\right)\right) +10\sin\left(2\tan^{-1}(2)\right) \]

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Principal value range: \[ \cot^{-1}x\in(0,\pi) \] Useful identity: \[ \sin(2\theta)=\frac{2\tan\theta}{1+\tan^2\theta} \]

Updated On: May 20, 2026

\(3\pi+7\)
\(7\)
\(4\pi+7\)
\(3\pi-5\)

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The Correct Option is C

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