Question

please say the answer fast

Answer 1

Heya!

Am Taking θ = α (For explaining Conveniently)

We know that : $Cos\alpha = 1 - 2Sin^2(\alpha/2)$

⇒ $1 - Cos\alpha = 2Sin^2(\alpha/2)$

We also know that : $Cos\alpha = 2Cos^2(\alpha/2) - 1$

⇒ $1 + Cos\alpha = 2Cos^2(\alpha/2)$

⇒ $\sqrt{\frac{1 - Cos\alpha}{1 + Cos\alpha}} = \sqrt{\frac{2Sin^2(\alpha/2)}{2Cos^2(\alpha/2)}} = Tan(\alpha/2)$

⇒ x = Tan(α/2)

⇒ $\frac{2x}{1 - x^2} = \frac{2Tan(\alpha/2)}{1 - Tan^2(\alpha/2)} = Tan\alpha$

So the Actual Answer is Tanθ

Option (3) is the Answer