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If \(\frac{\pi }{2}\leq x\leq \frac{3\pi }{4}\) , then \({\cos }^{-1}\left(\frac{12}{13}\cos x+\frac{5}{13}\sin x\right)…

Q1

If \(\frac{\pi }{2}\leq x\leq \frac{3\pi }{4}\) , then \({\cos }^{-1}\left(\frac{12}{13}\cos x+\frac{5}{13}\sin x\right)\) is equal to

[JEE Main 2025, 23 Jan (Shift 1)]

a

\(x-{\tan }^{-1}\frac{4}{3}\)

b

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

c

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

d

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

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