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SSC CHSL 2023 PYQ — Question 54

SSC CHSL - 13 March 2023 - Shift 2 • Quantitative Aptitude • Q54

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If m=sec θ\theta-tan θ\theta and n = cosec θ\theta+ cot θ\theta, then what is the value of m + n(m-1)?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. -1.

m = sec θ - tan θ = (1 - sin θ)/cos θ

n = cosec θ + cot θ = (1 + cos θ)/sin θ

m + n(m - 1)

= m + nm - n

=1−sinθcosθ+1−sinθcosθ×1+cosθsinθ−1−sinθcosθ=\frac{1-sin\theta}{cos\theta}+\frac{1-sin\theta}{cos\theta}\times \frac{1+cos\theta}{sin\theta}-\frac{1-sin\theta}{cos\theta}

=sinθ−cosθ−1+1−sinθ+cosθ−cosθ×sinθsinθcosθ=\frac{sin θ - cos θ - 1 + 1 - sin θ + cos θ - cos θ × sin θ}{sin\theta cos\theta}

= (- cos θ × sin θ)/(sin θ × cos θ)

= - 1

Hence, the required value is - 1.