If cosθ + sec θ = 8, find the value of cos2θ + sec2θ.
Answer & explanation
Correct answer: option 3
Formula I → [ cosθ = \(\frac{1}{secθ}\)]
Formula II → [If x + \(\frac{1}{x}\) = n and x2 + \(\frac{1}{x^2}\) = n2 - 2 ]
cosθ + \(\frac{1}{secθ}\) = 8
⇒ cos2θ + \(\frac{1}{sec^2θ}\) = (8)2 - 2
⇒ cos2θ + sec2θ = 64 - 2 = 62