(C) We know the identity ${\tan ^{ - 1}}x + {\cot ^{ - 1}}x = \frac{\pi }{2}$.Given the equation ${\cot ^{ - 1}}x + {\tan ^{ - 1}}3 = \frac{\pi }{2}$.

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(C) We know the identity ${\tan ^{ - 1}}x + {\cot ^{ - 1}}x = \frac{\pi }{2}$.Given the equation ${\cot ^{ - 1}}x + {\tan ^{ - 1}}3 = \frac{\pi }{2}$.Comparing this with the identity ${\tan ^{ - 1}}x + {\cot ^{ - 1}}x = \frac{\pi }{2}$,we can see that the values must match.Therefore,$x = 3$.

Class 12 Mathematics Inverse Trigonometric Functions Basic Concepts of ITF

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If ${\cot ^{ - 1}}x + {\tan ^{ - 1}}3 = \frac{\pi }{2}$,then $x =$

A
$1/3$
B
$1/4$
C
$3$
D
$4$

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Inverse Trigonometric Functions

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Basic Concepts of ITF

Write the function in the simplest form: $\tan ^{-1}\left(\sqrt{\frac{1-\cos x}{1+\cos x}}\right), x < \pi$

Medium

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If $2 \tan^{-1}(\cos x) = \tan^{-1}(2 \operatorname{cosec} x)$,then the value of $x$ is

MediumMHT CET 2025

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Find the value of $\tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]$

Medium

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If $y = \sin^{-1}\left(\frac{2^{x+1}}{1+4^x}\right)$ and $\frac{dy}{dx} = \frac{2^{x+1} \log 2}{f(x)}$,then $f(0) = $ . . . . . .

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If ${\cot ^{ - 1}}x + {\tan ^{ - 1}}3 = \frac{\pi }{2}$,then $x =$

Similar Questions

Write the function in the simplest form: $\tan ^{-1}\left(\sqrt{\frac{1-\cos x}{1+\cos x}}\right), x < \pi$

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