AP EAMCET · Maths · Trigonometric Ratios & Identities
For all values of \(\theta\), the values of \(3-\cos \theta+\cos \left(\theta+\frac{\pi}{3}\right)\) lie in the interval :
- A \([-2,3]\)
- B \([-2,1]\)
- C \([2,4]\)
- D \([1,5]\)
Answer & Solution
Correct Answer
(C) \([2,4]\)
Step-by-step Solution
Detailed explanation
\(3-\cos \theta+\cos \left(\theta+\frac{\pi}{3}\right)\) \(=3-\cos \theta+\cos \theta \cdot \cos \frac{\pi}{3}-\sin \theta \cdot \sin \frac{\pi}{3}\) \(=3-\cos \theta+\frac{1}{2} \cos \theta-\frac{\sqrt{3}}{2} \sin \theta\)…
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