- In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
- Given that
$$\sqrt { 2 } \sin \left( x + 45 ^ { \circ } \right) = \cos \left( x - 60 ^ { \circ } \right)$$
show that
$$\tan x = - 2 - \sqrt { 3 }$$
- Hence or otherwise, solve, for \(0 \leqslant \theta < 180 ^ { \circ }\)
$$\sqrt { 2 } \sin ( 2 \theta ) = \cos \left( 2 \theta - 105 ^ { \circ } \right)$$