4.10: Trigonometric identity and equation

0606/23/M/J/26 — Question 6 · 8 marks

(a)
Show that \(\dfrac{\sin\theta}{\sec\theta-\tan\theta}+\dfrac{\sin\theta}{\sec\theta+\tan\theta}=2\tan\theta\).
[3]
(b)
Hence solve the equation obtained by setting the left-hand side equal to \(\cos\theta\) for \(0\leqslant\theta\leqslant360^\circ\).
[5]