If cosθ + sec θ = 11 , find the value of cos3θ + sec3θ .
Answer & explanation
Correct answer: option 4
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