Question 10 - A-Level Maths

Exam Board	SPS
Module	SPS SM Pure (SPS SM Pure)
Year	2020
Session	October
Topic	Addition & Double Angle Formulae

10.

Prove that $$\cos ^ { 2 } \left( \theta + 45 ^ { \circ } \right) - \frac { 1 } { 2 } ( \cos 2 \theta - \sin 2 \theta ) \equiv \sin ^ { 2 } \theta .$$
Hence solve the equation $$6 \cos ^ { 2 } \left( \frac { 1 } { 2 } \theta + 45 ^ { \circ } \right) - 3 ( \cos \theta - \sin \theta ) = 2$$ for $- 90 ^ { \circ } < \theta < 90 ^ { \circ }$.