CUET · MATHS · PYQ PAPER 2023
\(\cos ^{-1}\left(\frac{3}{5} \cos x+\frac{4}{5}\ sinx \right)=\)
- A \(x+\tan ^{-1}\left(\frac{4}{3}\right)\)
- B \(x-\tan ^{-1}\left(\frac{4}{3}\right)\)
- C \(2 x+\tan ^{-1}\left(\frac{4}{3}\right)\)
- D \(2 x-\tan ^{-1}\left(\frac{4}{3}\right)\)
Answer & Solution
Correct Answer
(B) \(x-\tan ^{-1}\left(\frac{4}{3}\right)\)
Step-by-step Solution
Detailed explanation
\( \text{Let } \alpha = \tan^{-1}\left(\frac{4}{3}\right) \). Then \( \cos \alpha = \frac{3}{5} \) and \( \sin \alpha = \frac{4}{5} \). \( \cos^{-1}\left(\frac{3}{5} \cos x+\frac{4}{5}\sin x\right) = \cos^{-1}(\cos \alpha \cos x + \sin \alpha \sin x) \)…
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