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Q.

The maximum value of fx=sin2x1+cos2xcos2x1+sin2xcos2xcos2xsin2xcos2xsin2x,x∈R is:

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a

5

b

7

c

34

d

5

answer is D.

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Detailed Solution

The given determinent fx=sin2x1+cos2xcox2x1+sin2xcos2xcox2xsin2xcos2xsin2x                                                =21+cos2xcox2x2cos2xcox2x1cos2xsin2x        C1→C1+C2                                                =0102cos2xcox2x1cos2xsin2x      R1→R1−R2Expand the determinant                     fx=2sin2x−cos2xThe maximum value of  acosx+bsinx is a2+b2Hence maximum  value of fx=22+1=5
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