| Exam Board | Edexcel |
|---|
| Module | C34 (Core Mathematics 3 & 4) |
|---|
| Year | 2017 |
|---|
| Session | January |
|---|
| Topic | Addition & Double Angle Formulae |
|---|
8. (a) Using the trigonometric identity for \(\tan ( A + B )\), prove that
$$\tan 3 x = \frac { 3 \tan x - \tan ^ { 3 } x } { 1 - 3 \tan ^ { 2 } x } , \quad x \neq ( 2 n + 1 ) 30 ^ { \circ } , \quad n \in \mathbb { Z }$$
(b) Hence solve, for \(- 30 ^ { \circ } < x < 30 ^ { \circ }\),
$$\tan 3 x = 11 \tan x$$
(Solutions based entirely on graphical or numerical methods are not acceptable.)