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Question

The number of solutions of the equation 1+sinxsin2x2=0[π,π] is

A
zero
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B
1
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C
2
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D
3
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Solution

The correct option is A zero
Given, 1+sinxsin2x2=0
2+2sinxsin2x2=0
2+sinx(1cosx)=0
4+2sinx(1cosx)=0
4+2sinxsin2x=0
sin2x=2sinx+4
Above is not possible for any value of x as LHS has maximum value 1 and RHS has minimum value 2.
Hence, there is no solution.

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