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Question

The least value of 'a' for which 4sin x+11sin x=a has at least one solution in the interval (0,π/2) is


A

9

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B

8

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C

4

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D

1

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Solution

The correct option is A

9


f(x)=4sin x+11sin x=af(x)=4 cos xsin2 x+cos x(1sin x)2=cos x(1(1sin x)24sin2 x)f(x)=01(1sin x)24sin2 x=0 as cos x0 in(0,π2)
This gives sin x=23
Substituting Eq. (i), we get
a=9


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