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SSC CHSL 2022 PYQ — Question 61

SSC CHSL - 30 May 2022 - Shift 1 • Quantitative Aptitude • Q61

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If tan θ\theta + cot θ\theta = 4, then find the value of tan2 θ\theta + cot2 θ\theta

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 14

Calculations:

Let tan θ = x and cot θ = 1/x

⇒ x + 1/x = 4

Squaring both sides, we get

⇒ (x + 1/x)2 = 42

⇒ x2 + 1/x2 + 2 = 16

⇒ x2 + 1/x2 = 16 - 2 = 14

Hence,  tan2 θ\theta + cot2 θ\theta = 14