Question
If tan θ + cot θ = 5, then the value of
tan2 θ + cot2 θ + 2tan2 60° is:Solution
tan θ + cot θ = 5 Squaring both sides ⇒ tan2 θ + cot2 θ + 2 tanθ cotθ = 25 ⇒ tan2 θ + cot2 θ = 25 - 2 ⇒ tan2 θ + cot2 θ = 23 tan2 θ + cot2 θ + 2 tan2 60° ⇒ 23 + 2 × (√3)2 ⇒ 23 + 2 × 3 ⇒ 29
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