| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2015 |
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| Session | November |
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| Topic | Addition & Double Angle Formulae |
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6 The angles \(A\) and \(B\) are such that
$$\sin \left( A + 45 ^ { \circ } \right) = ( 2 \sqrt { } 2 ) \cos A \quad \text { and } \quad 4 \sec ^ { 2 } B + 5 = 12 \tan B$$
Without using a calculator, find the exact value of \(\tan ( A - B )\).