Standard +0.8 This question requires applying the tan addition formula twice, algebraic manipulation to simplify to a single variable, then solving a resulting equation. It involves multiple non-trivial steps including working with tan(θ±60°), using tan 60°=√3, and careful algebraic simplification. While the techniques are standard for P3, the multi-step nature and algebraic complexity place it moderately above average difficulty.
Use correct \(\tan(A \pm B)\) formula and express LHS in terms of \(\tan\theta\)
M1
Using \(\tan 60° = \sqrt{3}\) and \(\cot\theta = 1/\tan\theta\), obtain a correct equation in \(\tan\theta\) in any form
A1
Reduce the equation to one in \(\tan^2\theta\) only
M1
Obtain \(11\tan^2\theta = 1\), or equivalent
A1
Obtain answer \(16.8°\)
A1
## Question 3:
| Answer | Mark | Notes |
|--------|------|-------|
| Use correct $\tan(A \pm B)$ formula and express LHS in terms of $\tan\theta$ | M1 | |
| Using $\tan 60° = \sqrt{3}$ and $\cot\theta = 1/\tan\theta$, obtain a correct equation in $\tan\theta$ in any form | A1 | |
| Reduce the equation to one in $\tan^2\theta$ only | M1 | |
| Obtain $11\tan^2\theta = 1$, or equivalent | A1 | |
| Obtain answer $16.8°$ | A1 | |