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  4. The equation sin x+ sin y+ sin z=-3 for 0 ≤ x ≤ 2 π, 0 ≤ y ≤ 2 π, 0 ≤ z ≤ 2 π, has

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Q. The equation $\sin x+\sin y+\sin z=-3$ for $0 \leq x \leq 2 \pi$, $0 \leq y \leq 2 \pi, 0 \leq z \leq 2 \pi$, has

Trigonometric Functions

Solution:

Given equation i.e., $\sin x+\sin y+\sin z=-3$ is satisfied only when $x=y=z=\frac{3 \pi}{2}$, for $x, y, z \in[0,2 \pi]$.