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Question

Total number of solution of cos2x+3+12sinx341=0 in x[π,π] is :

A
6
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B
4
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C
7
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D
8
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Solution

The correct option is B 4
cos2x+(3+12)sinx341=0sin2x(3+12)sinx+34=04sin2x23sinx2sinx+3=02sinx(2sinx3)1(2sinx3)=0(2sinx3)(2sinx1)=0
sinx=12,32x=π6,5π6,π3,2π3
There are four solutions in [π,π].

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