If secθ + cosθ = 9, find the value of cos3θ + sec3θ.
Answer & explanation
Correct answer: option 3
Formula → [secθ = \(\frac{1}{cosθ}\) and cosθ = \(\frac{1}{secθ}\)]
⇒ cosθ + \(\frac{1}{cosθ}\) = 9
⇒ cos3θ + \(\frac{1}{cos^3θ}\) = (9)3 - 9 × 3
⇒ cos3θ + sec3θ = 729 - 27 = 702