If tanθ - cot θ = 12 , find the value of tan3θ - cot3θ .
Answer & explanation
Correct answer: option 1
Formula I → [ cotθ = \(\frac{1}{tanθ}\)]
Formula II → [If x - \(\frac{1}{x}\) = n and x3 - \(\frac{1}{x^3}\) = n3 + 3n]
tanθ - \(\frac{1}{tanθ}\) = 12
⇒ tan3θ - \(\frac{1}{tan^3θ}\) = (12)3 + 3 × 12
⇒ tan3θ - cot3θ = 1728 + 36 = 1764