The number of solutions of the equation 1+sinx⋅sin2x2=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+sinx⋅sin2x2=0 ⇒2+2sinx⋅sin2x2=0 ⇒2+sinx(1−cosx)=0 ⇒4+2sinx(1−cosx)=0 ⇒4+2sinx−sin2x=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.