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AP EAMCET · Maths · Trigonometric Ratios & Identities

The value of \(5 \cos \theta+3 \cos \left(\theta+\frac{\pi}{3}\right)+3\) lies between

  1. A -2 and 5
  2. B -1 and 8
  3. C -3 and 6
  4. D -4 and 10
Verified Solution

Answer & Solution

Correct Answer

(D) -4 and 10

Step-by-step Solution

Detailed explanation

Let \(f(\theta)=5 \cos \theta+3 \cos \left(\theta+\frac{\pi}{2}\right)+3\) \(\Rightarrow f(\theta)=5 \cos \theta+3 \cos \theta \cdot \frac{1}{2}-3 \sin \theta \cdot \frac{\sqrt{3}}{2}+3\) \(=\frac{13}{2} \cos \theta-\frac{3 \sqrt{3}}{2} \sin \theta+3\)…