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SSC CGL 2024 PYQ — Question 73

SSC CGL - 25 Sep 2024 - Shift 1 • Quantitative Aptitude • Q73

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Evaluate: 2tan⁡54∘cot⁡36∘−cot⁡41∘tan⁡49∘2 \frac{\tan 54^\circ}{\cot 36^\circ} - \frac{\cot 41^\circ}{\tan 49^\circ}

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 1.

2tan⁡54∘cot⁡36∘−cot⁡41∘tan⁡49∘2 \frac{\tan 54^\circ}{\cot 36^\circ} - \frac{\cot 41^\circ}{\tan 49^\circ}

=2tan⁡54∘cot⁡(90°−54°)−cot⁡41∘tan⁡(90°−41°)=2 \frac{\tan 54^\circ}{\cot (90° - 54°)} - \frac{\cot 41^\circ}{\tan (90° - 41°)}

=2tan⁡54∘tan⁡54∘−cot⁡41∘cot⁡41∘=2 \frac{\tan 54^\circ}{\tan 54^\circ} - \frac{\cot 41^\circ}{\cot 41^\circ}

= 2 × 1 - 1

= 2 - 1

= 1

Therefore, the required value is 1.