Standard +0.3 This question requires knowledge of the double angle formula for cot 2θ and converting it in terms of tan θ, then algebraic manipulation to form a quadratic. While it involves multiple steps (expressing cot in terms of tan, using double angle formula, forming and solving quadratic, finding solutions in range), these are standard techniques for P3 level. The 'hence solve' structure provides clear guidance on the method, making it slightly easier than average but still requiring competent execution of several techniques.
Use the tan \(2A\) formula to obtain an equation in \(\tan\theta\) only
M1
Obtain a correct horizontal equation
A1
Rearrange equation as a quadratic in \(\tan\theta\), e.g. \(3\tan^2\theta + 2\tan\theta - 1 = 0\)
A1
Solve for \(\theta\) (usual requirements for solution of quadratic)
M1
Obtain answer, e.g. \(18.4°\)
A1
Obtain second answer, e.g. \(135°\), and no others in the given interval
A1
[6]
## Question 3:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Use the tan $2A$ formula to obtain an equation in $\tan\theta$ only | M1 | |
| Obtain a correct horizontal equation | A1 | |
| Rearrange equation as a quadratic in $\tan\theta$, e.g. $3\tan^2\theta + 2\tan\theta - 1 = 0$ | A1 | |
| Solve for $\theta$ (usual requirements for solution of quadratic) | M1 | |
| Obtain answer, e.g. $18.4°$ | A1 | |
| Obtain second answer, e.g. $135°$, and no others in the given interval | A1 | [6] |
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