Question 8 - A-Level Maths

1. Show that the equation $$3 \sin \theta \tan \theta = 5 \cos \theta - 2$$ is equivalent to the equation $$( 4 \cos \theta - 3 ) ( 2 \cos \theta + 1 ) = 0$$ 8
(ii) Solve the equation $$3 \sin \theta \tan \theta = 5 \cos \theta - 2$$ for $- 180 ^ { \circ } \leq \theta \leq 180 ^ { \circ }$
8
Hence, deduce all the solutions of the equation $$3 \sin \left( \frac { 1 } { 2 } \theta \right) \tan \left( \frac { 1 } { 2 } \theta \right) = 5 \cos \left( \frac { 1 } { 2 } \theta \right) - 2$$ for $- 180 ^ { \circ } \leq \theta \leq 180 ^ { \circ }$, giving your answers to the nearest degree.
[0pt] [2 marks]