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If tan θ + cot θ = 6, then find the value of tan2 θ + cot2 θ.1. 362. 243. 264. 34 |
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Answer» Correct Answer - Option 4 : 34 Given: tan θ + cot θ = 6 Formula Used: (a + b)2 = a2 + b2 + 2ab tanθ × cotθ = 1 Calculations: tan θ + cot θ = 6 Squaring both sides, we get (tan θ + cot θ)2 = (6)2 ⇒ tan2 θ + cot2 θ + 2 × tanθ × cotθ = 36 ⇒ tan2 θ + cot2 θ + 2 × 1 = 36 ⇒ tan2 θ + cot2 θ = 36 – 2 ⇒ tan2 θ + cot2 θ = 34 ∴ The value of tan2 θ + cot2 θ is 34. |
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