The value of (2 cos² θ - 1) [ (1 + tan θ)/(1 - tan θ) + (1 - tan θ)/(1 + tan θ) ] is:

The value of (2 cos² θ - 1) [ (1 + tan θ)/(1 - tan θ) + (1…

The value of $(2 \cos^2 \theta - 1) \left[ \frac {1 + \tan \theta}{1 - \tan \theta} + \frac {1 - \tan \theta}{1 + \tan \theta} \right]$ is:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 2.

⇒ $(2 \cos^2 \theta - 1) \left[ \frac {1 + \tan \theta}{1 - \tan \theta} + \frac {1 - \tan \theta}{1 + \tan \theta} \right]$

⇒ $(2 \cos^2 \theta - 1) [ \frac {(1 + \tan \theta)^2 + (1 - \tan \theta)^2 }{1 - \tan^2\theta}]$

⇒ $(2 \cos^2 \theta - 1) [ \frac {2(1 + \tan^2 \theta)}{1 - \tan^2\theta}]$

As we know the formula

cos 2θ = cos²θ – sin² θ = 2 cos²θ – 1 = 1 – 2sin² = (1 – tan²θ)/(1 + tan²θ)

⇒ $\frac {(1 - \tan^2 \theta)}{1 + \tan^2\theta} [ \frac {2(1 + \tan^2 \theta)}{1 - \tan^2\theta}]$

⇒ 2