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Question

If p=sin2x+cos4x, then


A

34p1

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B

316p1/4

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C

14p1

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D

1p2

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Solution

The correct option is A

34p1


Find the range of p

The range of sinx and cosx is -1,1.

Therefore, the range of sin2x and cos2x is 0,1.

Given, p=sin2x+cos4x
=sin2x+(1-sin2x)2=sin4x+sin2x2sin2x+1=sin4xsin2x+1=sin2x-122+34p3/4

or it can also be written like
p=sin2x+cos4x=sin2x+cos2x(1-sin2x)=(sin2x+cos2x)sin2xcos2x=1sin2xcos2xp1
Therefore, 34p1

Hence 34p1 and therefore option (A) is correct.


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