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AP EAMCET · Maths · Trigonometric Equations

The general solution of the equation \(\sqrt{3-5 \sin x+\sin ^2 x}+\cos x=0\) is

  1. A \(n \pi+(-1)^n \frac{\pi}{6}, n \in Z\)
  2. B \(2 n \pi \pm \frac{\pi}{6}, n \in Z\)
  3. C \((2 n+1) \pi-\frac{\pi}{6}, n \in Z\)
  4. D \(2 n \pi \pm \frac{5 \pi}{6}, n \in Z\)
Verified Solution

Answer & Solution

Correct Answer

(C) \((2 n+1) \pi-\frac{\pi}{6}, n \in Z\)

Step-by-step Solution

Detailed explanation

Given equation, \[ \begin{gathered} \sqrt{3-5 \sin x+\sin ^2 x}+\cos x=0 \\ \Rightarrow \quad \sqrt{3-5 \sin x+\sin ^2 x}=-\cos x,\{\cos x\} \end{gathered} \] On squaring both sides, we get…