Mathematics

Evaluate ∫sec2θ dθ

Evaluate ∫sec2θ dθ
  • A.
    sec θ tan θ + k
  • B.
    tan θ + k
  • C.
    2sec θ + k
  • D.
    sec θ + k
Correct Answer: Option B
Explanation

∫sec2θ dθ = ∫ 1/cos2
∫(cos)-2 dθ,
let u = cos θ
∴∫u-2 = 1/u + c
∫cos θ = sin θ + c
∫sec-2θ = 1/u sin θ + c
= (sinθ / cosθ) + c
= Tan θ + c