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SSC CGL 2022 PYQ — Question 59

SSC CGL Tier II - Quant - 29 Jan 2022 • Quantitative Aptitude • Q59

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The value of 4 tan2 300+sin2 300 cos2 450+sec2 480−cot2 420cos370sin530+sin370cos530+tan180tan720\frac{4 \ tan^2 \ 30^0 + sin^2 \ 30^0 \ cos^2 \ 45^0 + sec^2 \ 48^0 - cot^2 \ 42^0}{cos37^0sin53^0 + sin37^0cos53^0+tan18^0tan72^0} is:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 5948\frac{59}{48}

4tan⁡230∘+sin⁡230∘cos⁡245∘+sec⁡248∘−cot⁡242∘cos⁡37∘sin⁡53∘+sin⁡37∘cos⁡53∘+tan⁡18∘tan⁡72∘\frac{4 \tan ^{2} 30^{\circ}+\sin ^{2} 30^{\circ} \cos ^{2} 45^{\circ}+\sec ^{2} 48^{\circ}-\cot ^{2} 42^{\circ}}{\cos 37^{\circ} \sin 53^{\circ}+\sin 37^{\circ} \cos 53^{\circ}+\tan 18^{\circ} \tan 72^{\circ}} = 43+18+sec248−tan2481+tan(90−72)tan72\frac{\frac{4}{3}+\frac{1}{8}+ sec^248 - tan^248}{1 + tan(90 - 72) tan72}

⇒ 43+18+12\frac{\frac{4}{3}+\frac{1}{8}+ 1}{2} = 59/48