JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(2y = {\left( {{{\cot }^{ - 1}}\,\left( {\frac{{\sqrt 3 \,\cos \,x + \sin \,x}}{{\cos \,x - \sqrt 3 \,\sin \,x}}} \right)} \right)^2}\) , \(x \in \left( {0,\frac{\pi }{2}} \right)\) then \(\frac{{dy}}{{dx}}\) is equal to
- A \(\frac{\pi }{6} - x\)
- B \(\frac{\pi }{3} - x\)
- C \(x - \frac{\pi }{6}\)
- D \(2x - \frac{\pi }{3}\)
Answer & Solution
Correct Answer
(D) \(2x - \frac{\pi }{3}\)
Step-by-step Solution
Detailed explanation
Consider \({\cot ^{ - 1}}\left( {\frac{{\frac{{\sqrt 3 }}{2}\cos x + \frac{1}{2}\sin x}}{{\frac{1}{2}\sin x - \frac{{\sqrt 3 }}{2}\sin x}}} \right)\)…
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