| Exam Board | Edexcel |
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| Module | C34 (Core Mathematics 3 & 4) |
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| Year | 2015 |
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| Session | January |
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| Topic | Addition & Double Angle Formulae |
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7. (a) Given that
$$2 \cos ( x + 30 ) ^ { \circ } = \sin ( x - 30 ) ^ { \circ }$$
without using a calculator, show that
$$\tan x ^ { \circ } = 3 \sqrt { 3 } - 4$$
(b) Hence or otherwise solve, for \(0 \leqslant \theta < 180\),
$$2 \cos ( 2 \theta + 40 ) ^ { \circ } = \sin ( 2 \theta - 20 ) ^ { \circ }$$
Give your answers to one decimal place.