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Value of \(\cos ^{-1}\left[\frac{12}{13} \cos x+\frac{5}{13} \sin x\right]\) is \(\left(x \in\left[\frac{\pi}{2}, \frac{…

Q1

Value of \(\cos ^{-1}\left[\frac{12}{13} \cos x+\frac{5}{13} \sin x\right]\) is \(\left(x \in\left[\frac{\pi}{2}, \frac{3\pi}{4}\right]\right)\)

[JEE Main 2025]

a

\(x+\tan ^{-1} \frac{12}{13}\)

b

\(x-\tan ^{-1} \frac{12}{13} \)

c

\(x-\tan ^{-1} \frac{5}{12}\)

d

\(x+\tan ^{-1}\left(\frac{4}{5}\right)\)

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