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SSC CGL 2022 PYQ — Question 73

SSC CGL - 12 April 2022 - Shift 3 • Quantitative Aptitude • Q73

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If 2ksin30°cos30°cot60° = cot⁡230∘sec⁡60∘tan⁡45∘csc⁡245∘csc⁡30∘\frac{\cot^2 30^\circ \sec 60^\circ \tan 45^\circ}{\csc^2 45^\circ \csc 30^\circ} , then find the value of k.

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 3

2ksin30°cos30°cot60° = cot⁡230∘sec⁡60∘tan⁡45∘csc⁡245∘csc⁡30∘\frac{\cot^2 30^\circ \sec 60^\circ \tan 45^\circ}{\csc^2 45^\circ \csc 30^\circ}

⇒ 2k × (1/2) × (31/2/2) × (1/31/2) = (3 × 2 × 1)/(2 × 2)

⇒  2k × (1/4) = 3/2

⇒ 2k × (1/2) = 3

⇒ k = 3