Standard +0.3 This is a standard trig equation requiring conversion of cot to tan, forming a quadratic in tan x, and solving within a given interval. While it involves multiple steps (rewriting cot x as 1/tan x, multiplying through, solving quadratic, finding angles), these are routine techniques for A-level. The algebraic manipulation is straightforward and the question type is common in textbooks, making it slightly easier than average.
6 In this question you must show detailed reasoning.
Solve the equation \(\tan x - 3 \cot x = 2\) for values of \(x\) in the interval \(0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }\).
Multiplying through by \(\tan x\) (M1) OR replacing \(\tan x\) with \(\frac{\sin x}{\cos x}\) and \(\cot x\) with \(\frac{\cos x}{\sin x}\)
M1
Two valid methods
Equation with 3 terms on one side and zero on other
M1
Solving 3-term equation AND getting both values of \(\tan x\) by valid method (factorisation, formula or completing square)
M1
Any two correct angles
A1
Subject to at least M2
All roots, no additional solutions; \(72°/252°\) and over-specified answers e.g. \(71.565°/251.565°\) allowed
A2
Subject to M3
## Question 6:
| Multiplying through by $\tan x$ (M1) OR replacing $\tan x$ with $\frac{\sin x}{\cos x}$ and $\cot x$ with $\frac{\cos x}{\sin x}$ | M1 | Two valid methods |
| Equation with 3 terms on one side and zero on other | M1 | |
| Solving 3-term equation AND getting both values of $\tan x$ by valid method (factorisation, formula or completing square) | M1 | |
| Any two correct angles | A1 | Subject to at least M2 |
| All roots, no additional solutions; $72°/252°$ and over-specified answers e.g. $71.565°/251.565°$ allowed | A2 | Subject to M3 |
6 In this question you must show detailed reasoning.
Solve the equation $\tan x - 3 \cot x = 2$ for values of $x$ in the interval $0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }$.
\hfill \mbox{\textit{OCR MEI Paper 3 2024 Q6 [5]}}