SSC CHSL 2019 PYQ — Question 60

The Correct Answer is option 2 i.e. cosecθ.

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

secθ = 1/cosθ

1- sin²θ = cos²θ

Use these values in the given expression

⇒ ${cot\theta}\over(1-sin\theta)(sec\theta+tan\theta)$

⇒ ${cot\theta}\over{{(1-sin\theta)}{({1\over cos\theta}}+{sin\theta \over cos\theta}})$

 ⇒ ${cot\theta}\over{{(1-sin\theta)}({1-sin\theta \over cos\theta}})$

 ⇒ ${{cos\theta}\over sin\theta}{{{cos\theta}\over({1-sin^2\theta})}}$

 ⇒ ${{cos^2\theta}\over sin\theta cos^2\theta}$

 ⇒ ${1\over sin\theta} = cosec\theta$