Question

Convert into simplest form: tan (θ - 14π)

Answer 1

we have to convert into simplest form of tan (θ - 14π)

we know, tan(2nπ - θ) = -tanθ
tan(-θ) = -tanθ


so, tan(θ - 14π) = tan{-(14π - θ)}

= -tan(14π - θ) [ as tan(-θ) = -tanθ]

= - tan(7 × 2π - θ)

= tanθ [ as tan(2nπ - θ) = -tanθ, where n is integer ]

hence, simplest form is tanθ