Question 6 - A-Level Maths

6 Prove that

\(\frac { \sin 2 \theta } { 2 \tan \theta } + \sin ^ { 2 } \theta = 1\),
\(\quad \sin \left( x + 45 ^ { \circ } \right) = \cos \left( x - 45 ^ { \circ } \right)\).