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SSC Selection Post 2022 PYQ — Question 66

SSC Selection Post - Graduation Level 2022 - 10 Feb 2022 - Shift 3 • Quantitative Aptitude • Q66

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The value of (tan25ocot65o−cosec265o)+cot261o−sec229osin25o+sin27o+sin29o+...+sin285o(tan25^ocot65^o-cosec^265^o)+cot^261^o-sec^229^o\over sin^25^o+sin^27^o+sin^29^o+...+sin^285^ois:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. −441-4\over41.

(tan25ocot65o−cosec265o)+cot261o−sec229osin25o+sin27o+sin29o+...+sin285o(tan25^ocot65^o-cosec^265^o)+cot^261^o-sec^229^o\over sin^25^o+sin^27^o+sin^29^o+...+sin^285^o

=(cot265°−cosec265°)+(tan229°−sec229°)(sin25°+sin285°)+(sin27°+sin283°)+(sin29°+sin281°)+....+sin245°={(cot^2 65° - cosec^2 65°) + (tan^2 29° - sec^2 29°)\over (sin^2 5° +sin^2 85°) + (sin^2 7° + sin^2 83°) + (sin^2 9° + sin^2 81°) + .... + sin^2 45°}

=−1−1(sin25°+cos25°)+(sin27°+cos27°)+(sin29°+cos29°)+....+sin245°={-1-1\over (sin^2 5° + cos^2 5°) + (sin^2 7° + cos^2 7°) + (sin^2 9° + cos^2 9°) + .... + sin^2 45°}

= (-2)/[20 + 1/2]

= (-2)/(41/2)

= -4/41