SSC CHSL 2021 PYQ — Question 67

The correct answer is Option 4 i.e. ${{sec^2\theta}}$

${{(1+cos\theta)(cosec\theta-cot\theta)sec\theta} \over sin\theta(1-sin\theta)(sec\theta+tan\theta)}=?$

= [(1 + cosθ){(1/sinθ) - (cosθ/sinθ)}(1/cosθ)]/[(sinθ(1 - sinθ){(1/cosθ) + (sinθ/cosθ)}]

= [(1 + cosθ){(1 - cosθ)/sinθ}(1/cosθ)]/[(sinθ)(1 - sinθ)(1 + sinθ)/cosθ]

= [(1 - cos²θ)/(sinθcosθ)]/[(1 - sin²θ)(sinθ/cosθ)]

= [sin²θ/(sinθcosθ)]/[(cos²θ)(sinθ/cosθ)]

= 1/cos²θ

= sec²θ