if cos4x + sin2x-p=0,p belongs to R has real solution then
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OC db if FL if DJ p FL if ghj
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h FL if FL jc FL jc GK jb FL if FL KB FL
Answered by
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cos
4
x+sin
2
x−p=0
∴cos
2
xcos
2
x+sin
2
x−p=0
∴cos
2
x(1−sin
2
x)+sin
2
x−p=0
∴cos
2
x−sin
2
xcos
2
x+sin
2
x−p=0
∴1−sin
2
xcos
2
x=p
∴1−
4
sin
2
2x
=p
0≤sin
2
2x≤1
∴
4
3
≤1−
4
sin
2
2x
≤1
∴
4
3
≤p≤1
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