Question

For any angle θ, sec θ = –sec (θ + 180°).

True

False

Answer 1

True.

Reason: sec θ = 1/cos θ and cos(θ + 180°) = −cos θ, so
sec(θ + 180°) = 1/cos(θ + 180°) = 1/(−cos θ) = −sec θ,
which gives sec θ = −sec(θ + 180°). (Both sides are only defined when cos θ ≠ 0.)