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Question
Prove that:
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Solution
\[ = \frac{\frac{\cos(x - a)}{\sin(x - a)} + \frac{\sin(x - b)}{\cos(x - b)}}{\cos(a - b)}\]
\[ = \frac{\cos(x - b) \cos(x - a) + \sin(x - a) \sin(x - b)}{\cos(a - b) \sin(x - a) \cos(x - b)}\]
\[ = \frac{\cos(x - b - x + a)}{\cos(a - b) \sin(x - a) \cos(x - b)} (\text{ Using }\cos(A - B) = \cos A \cos b B + \sin A \sin B)\]
\[ = \frac{\cos(a - b)}{\cos(a - b) \sin(x - a) \cos(x - b)}\]
\[ = \frac{1}{\sin(x - a) \cos(x - b)} \]
= RHS
Hence proved .
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