If cosθ - sec θ = 8 , find the value of cos3θ - sec3θ .
Answer & explanation
Correct answer: option 3
Formula I → [ sec = \(\frac{1}{cosθ}\)]
Formula II → [If x - \(\frac{1}{x}\) = n and x3 - \(\frac{1}{x^3}\) = n3 + 3n]
cosθ - \(\frac{1}{cosθ}\) = 8
⇒ cos3θ - \(\frac{1}{cos^3θ}\) = (8)3 + 3 × 8
⇒ cos3θ - sec3θ = 512 + 24 = 536