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Question

Number of ordered pairs (x,y) which satisfies x4+18x2=sin2ycos2y ; where y[0,2π] is

A
2
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B
4
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C
6
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D
8
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Solution

The correct option is D 8
x4+18x2=sin2ycos2yx4+1x2=2(2sinycosy)2x2+1x2=2sin22yL.H.S=x2+1x22 (a+b2ab)R.H.S=2sin22y2
For equation to have solution
L.H.S=R.H.S=2

L.H.S=2x2+1x2=2x42x2+1=0(x21)2=0x=±1

R.H.S=2sin22y=1=sin2π22y=nπ±π2, nZy=nπ2±π4
In y[0,2π], y={π4,3π4,5π4,7π4}

Hence, number of possible ordered pairs for (x,y)=8

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