## Question 4:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\cos 2\theta = \sin\theta$ | | |
| $\Rightarrow 1 - 2\sin^2\theta = \sin\theta$ | M1 | $\cos 2\theta = 1 - 2\sin^2\theta$ o.e. substituted |
| $\Rightarrow 1 - \sin\theta - 2\sin^2\theta = 0$ | M1 | forming quadratic (in one variable) $= 0$ |
| | A1 | correct quadratic www |
| $\Rightarrow (1-2\sin\theta)(1+\sin\theta) = 0$ | M1 | factorising or solving quadratic |
| $\Rightarrow \sin\theta = \frac{1}{2}$ or $-1$ | A1 | $\frac{1}{2},\ -1$ o.e. www |
| $\Rightarrow \theta = \frac{\pi}{6},\ \frac{5\pi}{6},\ \frac{3\pi}{2}$ | A2,1,0 [7] | cao; penalise extra solutions in the range |

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