| Exam Board | Edexcel |
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| Module | C34 (Core Mathematics 3 & 4) |
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| Year | 2018 |
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| Session | June |
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| Topic | Reciprocal Trig & Identities |
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12. (a) Show that
$$\cot x - \tan x \equiv 2 \cot 2 x , \quad x \neq 90 n ^ { \circ } , n \in \mathbb { Z }$$
(b) Hence, or otherwise, solve, for \(0 \leqslant \theta < 180 ^ { \circ }\)
$$5 + \cot \left( \theta - 15 ^ { \circ } \right) - \tan \left( \theta - 15 ^ { \circ } \right) = 0$$
giving your answers to one decimal place.
[0pt]
[Solutions based entirely on graphical or numerical methods are not acceptable.]