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SSC CHSL 2021 PYQ — Question 67

SSC CHSL - 13 April 2021 - Shift 2 • Quantitative Aptitude • Q67

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If 0º < θ < 90º, then (1+cos⁡θ)(cosecθ−cot⁡θ)sec⁡θsin⁡θ(1−sin⁡θ)(sec⁡θ+tan⁡θ)=?\frac{(1+\cos \theta)(cosec \theta-\cot \theta)\sec \theta}{\sin \theta(1-\sin\theta)(\sec \theta+\tan \theta)}=? 

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Correct answer: A

Explanation

The correct answer is option 1 i.e.  sec2θsec^2θ.

(1+cos⁡θ)(cosecθ−cot⁡θ)sec⁡θsin⁡θ(1−sin⁡θ)(sec⁡θ+tan⁡θ)\frac{(1+\cos \theta)(cosec \theta-\cot \theta)\sec \theta}{\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)/sinθ × 1/cosθ]/[sinθ (1 – sin2θ)/cosθ]

⇒ (sin2θ/sinθ × 1/cosθ)/(sinθ × cos2θ/cosθ)

⇒ (sinθ/cosθ)/(sinθ × cosθ)

⇒ 1/cos2θ 

⇒ sec2θ