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SSC CGL 2025 PYQ — Question 30

SSC CGL Tier II - 20 January 2025 - Shift I • Quantitative Aptitude • Q30

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If cos27° = pq\frac p q, then find the value of cosec27° - cos63°

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Correct answer: A

Explanation

The correct answer is option 1 i.e. p2qq2−p2\frac{p^2}{q\sqrt{q^2-p^2}}.

cos 27° = p/q = Base/Hypotenuse

Perpendicular = √(Hypotenuse2 - Base2) = √(q2 - p2)

Now, cosec27° - cos63°

= cosec27° - sin27°

=qq2−p2−q2−p2q=\frac{q}{\sqrt{q^2-p^2}}-\frac{\sqrt{q^2-p^2}}{q}

=p2qq2−p2=\frac{p^2}{q\sqrt{q^2-p^2}}

Therefore, the required value is p2qq2−p2\frac{p^2}{q\sqrt{q^2-p^2}}.