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SSC CGL 2024 PYQ — Question 65

SSC CGL - 19 Sep 2024 - Shift 1 • Quantitative Aptitude • Q65

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If sinA + cosA = 3\sqrt3, then find the value of tanA+ cotA + 2sinAcosA.

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 3.

sinA + cosA = √3

⇒ (sinA + cosA)2 = (√3)2

⇒ sin2A + 2sinAcosA + cos2A = 3

⇒ 1 + 2sinAcosA = 3   [∵ sin2A + cos2A = 1]

⇒ 2sinAcosA = 2

⇒ sinAcosA = 2/2 = 1

Now, tanA+ cotA + 2sinAcosA

= (sinA/cosA) + (cosA/sinA) + 2

= 1/(sinAcosA) + 2

= 1/1 + 2

= 1 + 2

= 3

Therefore, the value of tanA+ cotA + 2sinAcosA is 3.