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AP EAMCET · Maths · Trigonometric Equations

The number of values of \(x\) with \(0 \leq x \leq 2 \pi\) satisfying the equation \(\sin x+\sin 2 x+\sin 3 x=\cos x+\cos 2 x+\cos 3 x\) is

  1. A 7
  2. B 6
  3. C 5
  4. D 4
Verified Solution

Answer & Solution

Correct Answer

(C) 5

Step-by-step Solution

Detailed explanation

\((\sin x+\sin 3 x)+\sin 2x = (\cos x+\cos 3 x)+\cos 2x\) \(2\sin 2x \cos x + \sin 2x = 2\cos 2x \cos x + \cos 2x\) \(\sin 2x (2\cos x + 1) = \cos 2x (2\cos x + 1)\) \((2\cos x + 1)(\sin 2x - \cos 2x) = 0\) Case 1: \(2\cos x + 1 = 0 \Rightarrow \cos x = -\frac{1}{2}\)…