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A solution of the equation $(1 - \tan θ) (1 + \tan θ) \sec^{2} θ + 2^{\tan^{2} θ} = 0$ which $θ$ lies in the interval $(- π / 2, π / 2)$ is given by

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θ=0

θ=π3

θ=-π3

θ=π6

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detailed solution

Correct option is B

(1−tan⁡θ)(1+tan⁡θ)sec2⁡θ+2tan2⁡θ=0⇒1−tan4⁡θ+2tan2⁡θ=0⇒2t=t2−1 where t=tan2⁡θBy inspection (or by graph) we findy=2t and y=t2−1 intersect in t=3⇒ tan2⁡θ=3⇒ tan⁡θ=±3⇒θ=±π/3

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A solution of the equation (1−tan⁡θ)(1+tan⁡θ)sec2⁡θ+2tan2⁡θ=0 which θ lies in the interval (−π/2,π/2) is given by

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Ready to Test Your Skills?

free study material

A solution of the equation $(1 - \tan θ) (1 + \tan θ) \sec^{2} θ + 2^{\tan^{2} θ} = 0$ which $θ$ lies in the interval $(- π / 2, π / 2)$ is given by