If cosθ + sec θ = 6 , find the value of cos3θ + sec3θ .
Answer & explanation
Correct answer: option 2
Formula I → [ secθ = \(\frac{1}{cosθ}\)]
Formula II → [If x + \(\frac{1}{x}\) = n and x3 + \(\frac{1}{x^3}\) = n3 - 3n]
cosθ + \(\frac{1}{cosθ}\) = 6
⇒ cos3θ + \(\frac{1}{cos^3θ}\) = (6)3 - 3 × 6
⇒ cos3θ + sec3θ = 216 - 18 = 198