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Question

The equation cos2x+asinx=2a7 has a solution for

A
all a
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B
a>6
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C
a<2
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D
a[2,6]
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Solution

The correct option is B a[2,6]
Given equation is cos2x+asinx=2a7

12sin2x+asinx=2a7

2sin2xasinx+2a8=0

We have a formula for solving quadratic equation ax2+bx+c=0 is

x=b±b24ac2a

sinx=a±a216(a4)4=a±(a8)4

sinx=a42 or sinx=2 (not possible)

sinx=a42

1sinx1

1a421

2a6a[2,6]

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