If cosθ + sec θ = 11 , find the value of cos3θ + sec3θ .

1280 1078 1198 1298

1298

Formula I → [ sec = \(\frac{1}{cosθ}\)] Formula II → [If x + \(\frac{1}{x}\) = n and x3 + \(\frac{1}{x^3}\) = n3 - 3n] cosθ + \(\frac{1}{cosθ}\) = 11 ⇒ cos3θ + \(\frac{1}{cos^3θ}\) = (11)3 - 3 × 11 ⇒ cos3θ + sec3θ = 1331 - 33 = 1298