Question

Convert into simplest form: sec (4π - θ)

Answer 1

we have to convert simplest form of sec(4π - θ)

we know, sec(2π + θ) = secθ

sec(2π - θ) = secθ

[ because in fourth quadrant cosine and secant be positive. (360° - θ) or (2π - θ) lies in 4th quadrant so, sec(2π - θ) = secθ ]

now, sec(4π - θ) = sec{2π + (2π - θ)}

= sec(2π - θ)

= secθ [ as sec(2π - θ) = secθ]

hence, simplest form is secθ