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COMEDK · Maths · 9. Trigonometric Equations

If \(\sin 2 x=4 \cos x\), then \(x\) is equal to

  1. A \(\dfrac{n \pi}{2} \pm \dfrac{\pi}{4}, n \in Z\)
  2. B no value
  3. C \(n \pi+(-1)^{n} \dfrac{\pi}{4}, n \in Z \quad\)
  4. D \(2 n \pi \pm \dfrac{\pi}{2}, n \in Z\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2 n \pi \pm \dfrac{\pi}{2}, n \in Z\)

Step-by-step Solution

Detailed explanation

Given the equation \(\sin 2x = 4 \cos x\). Using the double angle identity \(\sin 2x = 2 \sin x \cos x\), the equation becomes: \(2 \sin x \cos x = 4 \cos x\) Rearranging the terms: \(2 \sin x \cos x - 4 \cos x = 0\) \(2 \cos x (\sin x - 2) = 0\) This implies either…