Verified Solution • 2025–26 Session moderate QJEEM25Ma12fa: JEE Main 2025 Mathematics - Class 12 JEEM25Ma12fa Solution: If , then is equal to If π2≤x≤3π4\frac{\pi}{2} \leq x \leq \frac{3 \pi}{4}2π≤x≤43π , then cos−1(1213cosx+513sinx)\cos ^{-1}\left(\frac{12}{13} \cos x+\frac{5}{13} \sin x\right)cos−1(1312cosx+135sinx) is equal to Multiple Choice Options A x+tan−1512x+\tan ^{-1} \frac{5}{12}x+tan−1125 B x−tan−143x-\tan ^{-1} \frac{4}{3}x−tan−134 C x+tan−145x+\tan ^{-1} \frac{4}{5}x+tan−154 D x−tan−1512x-\tan ^{-1} \frac{5}{12}x−tan−1125 Step-by-Step Verified Solution amp;π2≤x≤3π4amp;cos−1(1213cosx+512sinx)amp;cos−1(cosxcosα+sinxsinα)amp;cos−1(cos(x−α))amp;⇒x−α because x−α∈(−π2,π2)amp;⇒x−tan−1512\begin{aligned}& \frac{\pi}{2} \leq x \leq \frac{3 \pi}{4} \\& \cos ^{-1}\left(\frac{12}{13} \cos x+\frac{5}{12} \sin x\right) \\& \cos ^{-1}(\cos x \cos \alpha+\sin x \sin \alpha) \\& \cos ^{-1}(\cos (x-\alpha)) \\& \Rightarrow x-\alpha \text { because } x-\alpha \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \\& \Rightarrow x-\tan ^{-1} \frac{5}{12}\end{aligned}amp;2π≤x≤43πamp;cos−1(1312cosx+125sinx)amp;cos−1(cosxcosα+sinxsinα)amp;cos−1(cos(x−α))amp;⇒x−α because x−α∈(−2π,2π)amp;⇒x−tan−1125 Related Learning Resources & Exam Preparation JEE Main PYQ Question Bank Browse year-wise authentic previous years' questions with solutions Authentic CBT Mock Tests Simulate official exam environment with live timer and percentile scoring