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TS 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 :

  1. A \([-2,3]\)
  2. B \([-2,1]\)
  3. C \([2,4]\)
  4. D \([1,5]\)
Verified Solution

Answer & Solution

Correct Answer

(C) \([2,4]\)

Step-by-step Solution

Detailed explanation

\(3-\cos \theta+\cos \left(\theta+\frac{\pi}{3}\right)\) \(=3-\cos \theta+\cos \theta \cdot \cos \frac{\pi}{3}-\sin \theta \cdot \sin \frac{\pi}{3}\) \(=3-\cos \theta+\frac{1}{2} \cos \theta-\frac{\sqrt{3}}{2} \sin \theta\)…