1.

\(\frac{{\cos \theta }}{{1 - \sin \theta }} - \frac{{\cos \theta }}{{1 + sin\theta }}\; = \;\sqrt {12} \) is satisfied by which one of the following values of θ?1). π/22). π/33). π/44). π/6

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 – b& 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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