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Question

For x(0,π), the equation sinx+2sin2xsin3x=3, has

A
infinitely many solutions
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B
three solutions
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C
one solution
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D
no solution
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Solution

The correct option is C no solution

sinx+2sin2xsin3x=3

sinx+4sinxcosx3sinx+4sin3x=3

sinx[2+4cosx+4(1cos2x)]=3

sinx[2(4cos2x4cosx+1)+1]=3

sinx[3(2cosx1)2]=3

sinx=1 and 2cosx1=0

x=π2 and x=π3

Which is not possible at same time.

Hence, no solution.


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