The possible value of p for which graph of the function f(x)=2p2−3ptan⁡x+tan2⁡x+1 does not lie below x -axis for all x∈−π2,π2 is

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answer is A.

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Detailed Solution

Let tan⁡x=t∈R y=t2−3pt+2p2+1,t∈RGraph does not lie below x- axis,∴ D≤0∴ 9p2−42p2+1≤0⇒ p2−4≤0⇒ p∈[−2,2]

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