- In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
- Given that
$$2 \sin \left( x - 60 ^ { \circ } \right) = \cos \left( x - 30 ^ { \circ } \right)$$
show that
$$\tan x = 3 \sqrt { 3 }$$
- Hence or otherwise solve, for \(0 \leqslant \theta < 180 ^ { \circ }\)
$$2 \sin 2 \theta = \cos \left( 2 \theta + 30 ^ { \circ } \right)$$
giving your answers to one decimal place.