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Question

For x(0,π), the equation sin x+2 sin 2x -sin 3x =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 D no solution

sin x+2 sin 2x-sin 3x =3
sinx+4sinxcosx3sinx+4sin3x=3sinx[2+4cosx+4(1cos2x)]=3sinx[2(4cos2x4cosx+1)+1]=33(2cosx1)2=3cosecx
Now R.H.S. 3
But L.H.S. < 3
Hence, no solution.


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