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Question

If 0x<π2, then the number of values of x for which sinxsin2x+sin3x=0, is :

A
3
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B
4
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C
2
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D
1
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Solution

The correct option is C 2
sinxsin2x+sin3x=0
sinx+sin3xsin2x=0
2sin2xcosxsin2x=0
sin2x(2cosx1)=0

Case-1 :
sin2x=0
x=0

Case-2 :
2cosx1=0
cosx=12
x=π3
Hence, x=0,π3
Number of values of x=2

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