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\(\frac{{\cos \theta }}{{1 - \sin \theta }} - \frac{{\cos \theta }}{{1 + sin\theta }}\; = \;\sqrt {12} \) is satisfied by which one of the following values of θ?1). π/22). π/33). π/44). π/6 |
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Answer» $(\frac{{\COS \theta }}{{1 - \sin \theta }} - \frac{{\cos \theta }}{{1 + sin\theta }}\; = \;\SQRT {12} \Rightarrow \;\frac{{\cos \theta (1 + \sin \theta ) - \cos \theta (1 - \sin \theta )}}{{1 - {{\sin }^2}\theta }}\; = \;2\sqrt 3 )$ (? (a + b)(a – b) = a2 – b2 & sin2 x + cos2 x = 1) ⇒ cosθ + cosθsin θ – cosθ + cosθsinθ = 2√3cos2θ ⇒ 2sinθcosθ = 2√3cos2θ ⇒ sinθ/cosθ = √3 (? tan x = sin x/cos x) ⇒ tan θ = √3 ⇒ θ = 60° = π/3 ∴ θ = π/3 |
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