The correct option is D 8
x4+18x2=sin2ycos2y⇒x4+1x2=2(2sinycosy)2⇒x2+1x2=2sin22yL.H.S=x2+1x2≥2 (∵a+b≥2√ab)R.H.S=2sin22y≤2
For equation to have solution
L.H.S=R.H.S=2
L.H.S=2⇒x2+1x2=2⇒x4−2x2+1=0⇒(x2−1)2=0⇒x=±1
R.H.S=2⇒sin22y=1=sin2π2⇒2y=nπ±π2, n∈Z⇒y=nπ2±π4
In y∈[0,2π], y={π4,3π4,5π4,7π4}
Hence, number of possible ordered pairs for (x,y)=8