For all real numbers where the expressions involved are defined

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

For all real numbers

x

where the expressions involved are defined, consider

\operatorname{sec} x - \tan x

. (i) Show that

\operatorname{sec} x - \tan x = \dfrac{\cos x}{1 + \sin x}

. (ii) Hence, state the domain of the identity obtained in part (i). (iii) Using the result of part (i), evaluate

\operatorname{sec}\, \dfrac{\pi}{6} - \tan \dfrac{\pi}{6}