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$Number of solution(s) of the equation sin 2 θ + \cos 2 θ = - \frac{1}{2}, θ \in [0, \frac{π}{2}], is$

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Correct option is B

Given that sin⁡2θ+cos2⁡θ=−12⇒2tan⁡θ1+tan2⁡θ+1−tan2⁡θ1+tan2⁡θ=−12⇒2tan⁡θ+1−tan2⁡θ1+tan2⁡θ=−12⇒tan2⁡θ−4tan⁡θ−3=0 It is a quadratic equation in terms of tan⁡θ⇒tan⁡θ=4±16+122 ∵tan⁡θ=−b±b2−4ac2a⇒tan⁡θ=2±7 Number of solution of the given equation is 1 since tanθ is positive

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