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SSC CHSL 2023 PYQ — Question 69

SSC CHSL - 07 Aug 2023 - Shift 4 • Quantitative Aptitude • Q69

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Simplify the given expression: sin232∘+sin258∘cos232∘+cos258∘+sin253∘+cos53∘sin37∘\frac{sin^232^{\circ} +sin^258^{\circ}}{cos^232{\circ}+cos^258^{\circ}}+sin^253^{\circ}+cos53^{\circ}sin37^{\circ}

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Correct answer: A

Explanation

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

sin232∘+sin258∘cos232∘+cos258∘+sin253∘+cos53∘sin37∘\frac{sin^232^{\circ} +sin^258^{\circ}}{cos^232{\circ}+cos^258^{\circ}}+sin^253^{\circ}+cos53^{\circ}sin37^{\circ}

We know that,

sin(90 - A) = cosA

⇒ sin232∘+sin2(90∘−32∘)cos2(90∘−58∘)+cos258∘+sin253∘+cos53∘sin(90∘−53∘)\frac{sin^232^{\circ} +sin^2(90^{\circ}-32^{\circ})}{cos^2(90^{\circ}-58^{\circ})+cos^258^{\circ}}+sin^253^{\circ}+cos53^{\circ}sin(90^{\circ}-53^{\circ})

⇒ sin232∘+cos232∘sin258∘+cos258∘+sin253∘+cos53∘cos53∘\frac{sin^232^{\circ} +cos^232^{\circ}}{sin^258^{\circ}+cos^258^{\circ}}+sin^253^{\circ}+cos53^{\circ}cos53^{\circ}

⇒ 11+sin253∘+cos253∘\frac{1}{1}+sin^253^{\circ}+cos^253^{\circ}

⇒ 1 + 1 = 2