If tanθ + cot θ = 9 , find the value of tan2θ + cot2θ .
Answer & explanation
Correct answer: option 4
Formula I → [ tanθ = \(\frac{1}{cotθ}\)]
Formula II → [If x + \(\frac{1}{x}\) = n and x2 + \(\frac{1}{x^2}\) = n2 - 2]
tanθ + \(\frac{1}{tanθ}\) = 9
⇒ tan2θ + \(\frac{1}{tan^2θ}\) = (9)2 - 2
⇒ tan2θ + cot2θ = 81 - 2 = 79