Standard +0.8 This question requires applying the double angle formula for cotangent (cot 2x = (cot²x - 1)/(2cot x)), substituting into the equation, and solving the resulting quadratic in cot x. While it involves multiple steps and manipulation of reciprocal trig functions, it follows a standard pattern for P3-level questions. The restricted domain adds minor complexity but the algebraic manipulation is straightforward once the substitution is made.
Use correct tan \(2A\) and cot \(A\) formulae to form an equation in tan \(x\)
M1
Obtain a correct equation in any form
A1
Reduce equation to the form \(\tan^2 x + 6\tan x - 3 = 0\), or equivalent
A1
Solve a three term quadratic in tan \(x\) for \(x\), as in Q1
M1
Obtain answer, e.g. \(24.9°\) (24.896...)
A1
Obtain second answer, e.g. \(98.8\) (98.794) and no others in the given interval
A1
[Ignore outside the given interval. Treat answers in radians as a misread.] Radian answers 0.43452, 1.7243
A1
6
Use correct tan $2A$ and cot $A$ formulae to form an equation in tan $x$ | M1 |
Obtain a correct equation in any form | A1 |
Reduce equation to the form $\tan^2 x + 6\tan x - 3 = 0$, or equivalent | A1 |
Solve a three term quadratic in tan $x$ for $x$, as in Q1 | M1 |
Obtain answer, e.g. $24.9°$ (24.896...) | A1 |
Obtain second answer, e.g. $98.8$ (98.794) and no others in the given interval | A1 |
[Ignore outside the given interval. Treat answers in radians as a misread.] Radian answers 0.43452, 1.7243 | A1 | 6 |