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SSC Selection Post 2024 PYQ — Question 52

SSC Selection Post - Higher Secondary Level - 20 Jun 2024 - Shift 2 • Quantitative Aptitude • Q52

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Evaluate 7(cosec24∘sec66∘)3+8(cot37∘tan53∘)4−(2sec14∘cosec76∘)2+(−3tan82∘cot8∘)37\left ( \frac{cosec 24^\circ}{sec 66^\circ} \right )^3+ 8\left (\frac{cot 37^\circ}{tan 53^\circ} \right )^4-\left ( 2\frac{sec 14^\circ}{cosec 76^\circ} \right )^2+ \left ( -3\frac{tan82^\circ}{cot8^\circ} \right )^3

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Correct answer: A

Explanation

The correct answer is Option 1  i.e. -16.

7(cosec24∘sec66∘)3+8(cot37∘tan53∘)4−(2sec14∘cosec76∘)2+(−3tan82∘cot8∘)37\left ( \frac{cosec 24^\circ}{sec 66^\circ} \right )^3+ 8\left (\frac{cot 37^\circ}{tan 53^\circ} \right )^4-\left ( 2\frac{sec 14^\circ}{cosec 76^\circ} \right )^2+ \left ( -3\frac{tan82^\circ}{cot8^\circ} \right )^3

=7(cosec24∘cosec24∘)3+8(cot37∘cot37∘)4−(2sec14∘sec14∘)2+(−3tan82∘tan82∘)3=7\left ( \frac{cosec 24^\circ}{cosec 24^\circ} \right )^3+ 8\left (\frac{cot 37^\circ}{cot 37^\circ} \right )^4-\left ( 2\frac{sec 14^\circ}{sec 14^\circ} \right )^2+ \left ( -3\frac{tan82^\circ}{tan82^\circ} \right )^3

= 7 × 13 + 8 × 14 - (2 × 1)2 + (-3 × 1)3

= 7 + 8 - 4 - 27

= -16