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Question: The equation \(\sin x + \sin y + \sin z = - 3\)for \(0 \leq x \leq 2\pi,0 \leq y \leq 2\pi,0 \leq z...

The equation sinx+siny+sinz=3\sin x + \sin y + \sin z = - 3for

0x2π,0y2π,0z2π,0 \leq x \leq 2\pi,0 \leq y \leq 2\pi,0 \leq z \leq 2\pi, has

A

One solution

B

Two sets of solution

C

Four sets of solution

D

No solution

Answer

One solution

Explanation

Solution

Given,f(x)=sin4x+cos4xf(x) = \sin^{4}x + \cos^{4}xis satisfied only when

x=y=z=3π2;x = y = z = \frac{3\pi}{2}; for x,y,z,[0,2π]x,y,z, \in \lbrack 0,2\pi\rbrack.