SSC CGL 2021 PYQ — Question 72

The correct answer is option 4 i.e. $\dfrac{1+\sin\theta}{1-\sin\theta}$

Given :

1 + 2 tan² θ + 2sinθsec²θ

Formula used :

sin²θ + cos²θ = 1        ---- (1)

a² - b² = (a + b)(a - b)       ---- (2)

Calculations :

⇒ 1 + 2 tan² θ + 2sinθsec²θ

It can also be written as

⇒ 1 + 2(sin²θ/cos²θ) + 2sinθ/cos²θ

⇒ (cos²θ + sin²θ + sin²θ + 2sinθ)/(cos²θ)

Using equation (1), we get

⇒ (1 + sin²θ + 2sinθ)/(cos²θ)

⇒ [(1 + sinθ)(1 + sinθ)]/[(1 - sin²θ)]

Using equation(1) and (2), we get

⇒ [(1 + sinθ)(1 + sinθ)]/[(1 + sinθ)(1 - sinθ)]

⇒ (1 + sinθ)/(1 - sinθ)