Mathematics

Problem

Let

\theta

be an acute angle of a right triangle. a. (i) Using the definitions of the primary trigonometric ratios, prove that

\dfrac{\sin \theta}{\cos \theta} = \tan \theta

. b. (ii) Hence or otherwise, simplify the expression

\dfrac{\sin \theta}{1-\cos \theta} + \dfrac{\sin \theta}{1+\cos \theta}

and express your result entirely in terms of

\tan \theta