Answer: 0π
Step-by-step explanation:
[tex]sin\bigg(\dfrac{3\pi}{2}+x\bigg)+sin\bigg(\dfrac{3\pi}{2}+x\bigg)=-2\\\\\\2sin\bigg(\dfrac{3\pi}{2}+x\bigg)=-2\\\\\\sin\bigg(\dfrac{3\pi}{2}+x\bigg)=-1\\\\\\\dfrac{3\pi}{2}+x\bigg=sin^{-1}(-1)\\\\\\\dfrac{3\pi}{2}+x=\dfrac{3\pi}{2}\\\\\\\large\boxed{x=0}[/tex]
