Q. For $x, y, z \in[0,2 \pi]$. The number of ordered triplets $(x, y, z)$ satisfying $16\left(\sin ^4 x\right)+2\left(\sin ^4 y\right)+$ $4\left(\sin ^4 z\right)-16(\sin x)(\sin y)(\sin z)+2=0$.
JEE AdvancedJEE Advanced 2019
Solution:
Given equation simplifies to
$ \left(4 \sin ^2 x-2 \sin ^2 z\right)^2+4(2 \sin x \cdot \sin z-\sin y)^2+
2\left(\sin ^2 y-1\right)^2=0 $
$ \therefore \sin ^2 y=1,2 \sin x \cdot \sin z=\sin y, 2 \sin ^2 x=\sin ^2 z$
