Question

solve: sin x+sin2x+sin3x+sin4x=0

Answer 1

sin x + sin 2x + sin 3x + sin 4x = 0


( sin 3x + sin x) + ( sin 2x + sin 4x ) = 0

2 sin 2x cos x + 2 Sin3x cosx= 0

2 [ sin 2x cos x + sin 3 x cos x ] =0

2 cos x [ sin 2x + sin 3x ] =0

2 cos x [ sin 5x/2 × cos x/2 ] = 0

●[1] cos x = 0

x = (2n + 1) $\frac{\pi}{2}$

● [2] sin5x/2 = 0

$\frac{5x}{2} = n\pi \\ \\ x = \frac{2n\pi}{5}$

●[3] cos x/2=0

$\frac{x}{2} = (2n + 1) \frac{\pi}{2} \\ \\ x = (2n + 1)$

Answer 2

Hope You Find It Helpful

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