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Question
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
Solution
tan θ + cot θ = 2 ....[Given]
∴ (tan θ + cot θ)2 = 4 .....[Squaring both sides]
∴ tan2θ + 2tan θ.cot θ + cot2θ = 4 ......[∵ (a + b)2 = a2 + 2ab + b2]
∴ tan2θ + 2(1) + cot2θ = 4 ......[∵ tan θ ⋅ cot θ = 1]
∴ tan2θ + cot2θ = 4 – 2
∴ tan2θ + cot2θ = 2
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