- In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
- Show that the equation
$$2 \tan \theta \left( 8 \cos \theta + 23 \sin ^ { 2 } \theta \right) = 8 \sin 2 \theta \left( 1 + \tan ^ { 2 } \theta \right)$$
may be written as
$$\sin 2 \theta \left( A \cos ^ { 2 } \theta + B \cos \theta + C \right) = 0$$
where \(A , B\) and \(C\) are constants to be found.
- Hence, solve for \(360 ^ { \circ } \leqslant x \leqslant 540 ^ { \circ }\)
$$2 \tan x \left( 8 \cos x + 23 \sin ^ { 2 } x \right) = 8 \sin 2 x \left( 1 + \tan ^ { 2 } x \right) \quad x \in \mathbb { R } \quad x \neq 450 ^ { \circ }$$