Question 10 - A-Level Maths

Exam Board	SPS
Module	SPS SM Pure (SPS SM Pure)
Year	2022
Session	June
Topic	Geometric Sequences and Series

10.

Sketch the graph of $y = \cos x$ in the interval $0 \leqslant x \leqslant 2 \pi$. State the values of the intercepts with the coordinate axes.
1. Given that $$\sin ^ { 2 } \theta = \cos \theta ( 2 - \cos \theta )$$ prove that $\cos \theta = \frac { 1 } { 2 }$.
2. Hence solve the equation $$\sin ^ { 2 } 2 x = \cos 2 x ( 2 - \cos 2 x )$$ in the interval $0 \leqslant x \leqslant \pi$
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