Standard +0.8 This question requires multiple sophisticated steps: applying the tan addition formula, using the double angle formula for cot 2θ, algebraic manipulation to form a quadratic in tan θ, and solving within a restricted domain. While the individual techniques are standard P3 content, the combination and the non-obvious path from the given form to a quadratic makes this moderately challenging, requiring more problem-solving insight than a routine exercise.
Use tan \(2A\) formula to express RHS in terms of \(\tan\theta\)
M1
Use tan \((A \pm B)\) formula to express LHS in terms of \(\tan\theta\)
M1
Using \(\tan 45° = 1\), obtain a correct horizontal equation in any form
A1
Reduce equation to \(2\tan^2\theta + \tan\theta - 1 = 0\)
A1
Solve a 3-term quadratic and find a value of \(\theta\)
M1
Obtain answer \(\theta = 26.6°\) and no other
A1
## Question 5:
| Answer | Mark | Guidance |
|--------|------|----------|
| Use tan $2A$ formula to express RHS in terms of $\tan\theta$ | M1 | |
| Use tan $(A \pm B)$ formula to express LHS in terms of $\tan\theta$ | M1 | |
| Using $\tan 45° = 1$, obtain a correct horizontal equation in any form | A1 | |
| Reduce equation to $2\tan^2\theta + \tan\theta - 1 = 0$ | A1 | |
| Solve a 3-term quadratic and find a value of $\theta$ | M1 | |
| Obtain answer $\theta = 26.6°$ and no other | A1 | |
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