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SSC CGL 2023 PYQ — Question 74

SSC CGL - 24 July 2023 - Shift 2 • Quantitative Aptitude • Q74

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If cosecθ + cotθ = m, find the value of m2−1m2+1\frac{m^2-1}{m^2+1}

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Correct answer: C

Explanation

The correct answer is option 3 i.e.  cos θ.

cosecθ + cotθ = m

So, (cosecθ - cotθ) = 1/m,

m2−1m2+1\frac{m^2-1}{m^2+1} = m(m−1m)m(m+1m)\frac{m(m-\frac{1}{m})}{m(m+\frac{1}{m})}

=(cosecθ+cotθ)−(cosecθ−cotθ)(cosecθ+cotθ)+(cosecθ−cotθ)\frac{(cosecθ + cotθ) - (cosecθ - cotθ)}{(cosecθ + cotθ) + (cosecθ - cotθ)}

= 2cotθ2cosecθ\frac{2cotθ}{2cosecθ}

= (cosθ/sinθ)/(1/sinθ)

= cosθ