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SSC CHSL 2021 PYQ — Question 74

SSC CHSL - 5 Aug 2021 - Shift 1 • Quantitative Aptitude • Q74

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The value of tan50∘+sec50∘cot⁡40∘+cosec40∘+cos⁡265∘+sin65∘cos25∘+tan30∘\frac{{tan50^\circ + sec50^\circ }}{{\cot 40^\circ + cosec40^\circ }} + {\cos ^2}65^\circ + sin65^\circ cos25^\circ + tan30^\circ

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Correct answer: B

Explanation

The correct answer is option 2 i.e.  6+33\frac{6+\sqrt{3}}{3}

 

tan50∘+sec50∘cot⁡40∘+cosec40∘+cos⁡265∘+sin65∘cos25∘+tan30∘\frac{{tan50^\circ + sec50^\circ }}{{\cot 40^\circ + cosec40^\circ }} + {\cos ^2}65^\circ + sin65^\circ cos25^\circ + tan30^\circ

⇒ {Cot (90 - 50)° + Cosec (90 - 50)°} / (Cot 40° + Cosec 40°) + cos2 65° + sin 65° sin (90 - 25)° + tan 30°

⇒ (Cot 40° + Cosec 40°) / (Cot 40° + Cosec 40°) + (cos2 65° + sin2 65°) + (1/√3)

⇒ 1 + 1 + (1/√3)

⇒ 2 + √3/3

⇒ 6+33\frac{6+\sqrt{3}}{3}