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Question: The equation \(\frac{\pi}{6}\) is satisfied, if ....

The equation π6\frac{\pi}{6} is satisfied, if .

A

7π6\frac{7\pi}{6}

B

sin⁡5x+sin⁡3x+sin⁡x=0\sin 5x + \sin 3x + \sin x = 0

C

⇒\Rightarrow

D

−sin⁡3x=sin⁡5x+sin⁡x=2sin⁡3xcos⁡2x- \sin 3x = \sin 5x + \sin x = 2\sin 3x\cos 2x

Answer

sin⁡5x+sin⁡3x+sin⁡x=0\sin 5x + \sin 3x + \sin x = 0

Explanation

Solution

θ\theta

θ=π10\theta = \frac{\pi}{10}

On solving, sin⁡θ=5−14\sin\theta = \frac{\sqrt{5} - 1}{4}

Either 4sin⁡4x=1−cos⁡4x=(1−cos⁡2x)(1+cos⁡2x)4\sin^{4}x = 1 - \cos^{4}x = (1 - \cos^{2}x)(1 + \cos^{2}x), (which is not possible) or cos x =⇒\Rightarrow

sin⁡2x[4sin⁡2x−1−(1−sin⁡2x)]=0\sin^{2}x\lbrack 4\sin^{2}x - 1 - (1 - \sin^{2}x)\rbrack = 0.