Standard +0.3 This question requires applying the tan(θ ± α) addition formula twice, algebraic manipulation to form a quadratic in tan θ, then solving. While it involves multiple steps, the techniques are standard and the path is clear once the addition formulae are applied. The algebraic manipulation is straightforward, making this slightly easier than average.
Use \(\tan(A \pm B)\) formula and obtain an equation in \(\tan\theta\)
M1
Using \(\tan 45° = 1\), obtain a horizontal equation in \(\tan\theta\) in any correct form
A1
Reduce the equation to \(7\tan^2\theta - 2\tan\theta - 1 = 0\), or equivalent
A1
Solve a 3-term quadratic for \(\tan\theta\)
M1
Obtain a correct answer, e.g. \(\theta = 28.7°\)
A1
Obtain a second answer, e.g. \(\theta = 165.4°\), and no others
A1
[6]
[Ignore answers outside the given interval. Treat answers in radians as a misread (0.500, 2.89).]
Use $\tan(A \pm B)$ formula and obtain an equation in $\tan\theta$ | M1 |
Using $\tan 45° = 1$, obtain a horizontal equation in $\tan\theta$ in any correct form | A1 |
Reduce the equation to $7\tan^2\theta - 2\tan\theta - 1 = 0$, or equivalent | A1 |
Solve a 3-term quadratic for $\tan\theta$ | M1 |
Obtain a correct answer, e.g. $\theta = 28.7°$ | A1 |
Obtain a second answer, e.g. $\theta = 165.4°$, and no others | A1 | [6] |
[Ignore answers outside the given interval. Treat answers in radians as a misread (0.500, 2.89).]