JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
The maximum value of \(3\,\cos \,\theta + 5\,\sin \,\left( {\theta - \frac{\pi }{6}} \right)\) for any real value of \(\theta \) is
- A \(\sqrt {19}\)
- B \(\frac{{\sqrt {79} }}{2}\)
- C \(\sqrt {34}\)
- D \(\sqrt {31}\)
Answer & Solution
Correct Answer
(A) \(\sqrt {19}\)
Step-by-step Solution
Detailed explanation
\(5\,\sin \,\left( {\theta \, - \,\frac{\pi }{6}} \right)\, + \,3\,\cos \,\theta \) \( = \,5\left( {\sin \,\theta \,\cos \frac{\pi }{6}\, - \,\cos \,\theta \sin \frac{\pi }{6}} \right)\, + \,3\cos \,\theta \)…
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