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General solution of the equation $2 \cos^{2} θ + 11 \sin θ = 7$ is

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θ=nπ+(−1)nπ6

θ=2nπ+π6

θ=nπ+(−1)nπ3

θ=2nπ+π3

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detailed solution

Correct option is A

We have 2cos2θ+11sinθ=7⇒2(1−sin2θ)+11sinθ=7⇒2sin2θ−11sinθ+5=0⇒(2sinθ−1)(sinθ−5)=0⇒sinθ=12,sinθ≠5⇒θ=nπ+-1nπ6,n∈z

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General solution of the equation 2cos2θ+11sinθ=7 is

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General solution of the equation $2 \cos^{2} θ + 11 \sin θ = 7$ is