The correct option is D 5
Given, sin3x2−cos3x22+sinx=cosx3
⇒(sinx2−cosx2)(1+sinx2cosx2)2(1+sinx2cosx2)=cos2x2−sin2x23⇒3(sinx2−cosx2)+2(sin2x2−cos2x2)=0⇒(sinx2−cosx2)(3+2sinx2+2cosx2)=0⇒sinx2=cosx2(∵sinθ+cosθ∈[−√2,√2])⇒tanx2=1⇒x2=nπ+π4, n∈Z⇒x=2nπ+π2
In [0,10π],
x=π2,5π2,9π2,13π2,17π2
∴ Number of solutions is 5.