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Question

The range of f(x)=sin2x+cos4x is

A
[12,1]
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B
[34,1]
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C
[0,1]
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D
[0,14]
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Solution

The correct option is B [34,1]
f(x)=sin2x+(1sin2x)2

=1+sin2x2sin2x+sin4x

=1sin2x(1sin2x)
=1sin2xcos2x

=1(sin2x2)2
sin2x[1,1]

sin22x[0,1]
[sin2x2]2[0,14]

0[sin2x2]214

0[sin2x2]214

11[sin2x2]2114

1f(x)34

f(x) lies in [34,1]

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