The range of θ for which the point (√3sinθ,√4cosθ) lies outside x24−y25=1 is
A
θ∈R
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B
θ∈R−{π4}
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C
θ∈R−{π2,0}
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D
θ∈R−{π4,0,π2}
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Solution
The correct option is Aθ∈R S1<0 is the condition for the point to lie outside the hyperbola. ⇒3sin2θ4−4cos2θ5−1<0⇒15sin2θ−16cos2θ−20<0⇒31sin2θ−36<0⇒sin2θ<3631∴θ∈R(∵sin2θ∈[0,1])