## Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| State $\frac{1}{\cos^2\theta} \times \frac{\cos\theta}{\sin\theta} = 8$ | B1 | OE involving $\sin\theta$ and $\cos\theta$ only |
| Attempt use of $\sin 2\theta$ identity to obtain $\sin 2\theta = k$ | M1 | |
| Obtain $\sin 2\theta = \frac{1}{4}$ | A1 | |
| Use correct process to find two values of $\theta$ between 0 and $\pi$ | M1 | Allow if working in degrees |
| Obtain 0.126 and 1.44 | A1 | AWRT |
| **Alternative:** State $\frac{1+\tan^2\theta}{\tan\theta} = 8$ | B1 | |
| Attempt solution of 3-term quadratic equation to find values of $\tan\theta$ | M1 | OE involving $\tan\theta$ only |
| Obtain $\tan\theta = \frac{8 \pm \sqrt{60}}{2}$ | A1 | OE |
| Solve $\tan\theta = \ldots$ to find two values of $\theta$ between 0 and $\pi$ | M1 | Allow if working in degrees |
| Obtain 0.126 and 1.44 | A1 | AWRT |

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