Answer:
Option B
Explanation:
We have,
sinx +sin 3x+sin 5x=0
⇒ sinx+sin5x+sinx=0
⇒ 2sin3xcos2x+sin3x=0
⇒ sin3x(2cos2x+1)=0
⇒ sin3x=0 or cos2x=−12=cos2π3
⇒ 3x=nπ or 2n=2nπ±2π3
⇒ x=nπ3 or x=nπ±π3
But, it is given that
xϵ[π2,3π2]
∴ x=2π3,π,4π3
∴ Number of solutions is 3.