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Q.

Match the following

 List I List  II
1Maximum value of sin4x+cos4xa3
2Maximum value of 1+8sin2⁡xcos2⁡xb4
3 minimum value of cos4⁡x−sin4⁡xc1
4 minimum value of4cos2⁡x+5sin2⁡xd-1

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a

1−d,2−a,3−b,4−c

b

1−b,2−d,3−a,4−c

c

1−a,2−c,3−b,4−d

d

1−c,2−a,3−d,4−b

answer is A.

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Detailed Solution

sin4x+cos4x=1-2sin2xcos2x=1-12sin22x∈12,1

1+8sin2⁡xcos2⁡x=1+2(2sinxcosx)2=1+sin22x∈1,2

cos4⁡x−sin4⁡x=cos2⁡x−sin2⁡x=cos2x∈-1,1

4cos2⁡x+5sin2⁡x=4+sin2x∈4,5

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