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The numbers of solutions of the pair of equations $2 \sin^{2} θ - \cos 2 θ = 0$ , $2 \cos^{2} θ - 3 \sin θ = 0$ in the interval $[0, 2 π]$ is

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Correct option is C

2sin2⁡θ−cos⁡2θ=0⇒ 1−cos⁡2θ−cos⁡2θ=0⇒cos⁡2θ=1/2⇒ 2cos2⁡θ−1=1/2⇒2cos2⁡θ=3/2So that from 2cos2⁡θ−3sin⁡θ=0, we havesin⁡θ=1/2⇒θ=π/6,5π/6 as θ∈[0,2π].

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The numbers of solutions of the pair of equations 2sin2⁡θ−cos⁡2θ=0, 2cos2⁡θ−3sin⁡θ=0 in the interval [0,2π] is

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The numbers of solutions of the pair of equations $2 \sin^{2} θ - \cos 2 θ = 0$ , $2 \cos^{2} θ - 3 \sin θ = 0$ in the interval $[0, 2 π]$ is