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Question
` ∫ cos mx cos nx dx `
Sum
Solution
` ∫ cos mx cos nx dx `
` = 1/2 ∫ 2 cos ( mx) cos ( nx ) dx `
\[ = \frac{1}{2}\int\left[ \cos \left( mx + nx \right) + \cos \left( mx - nx \right) \right]dx \left[ \therefore 2 \cos A \cos B = \cos \left( A + B \right) + \cos \left( A - B \right) \right]\]
\[ = \frac{1}{2}\left[ \frac{\sin \left( m + n \right)x}{m + n} + \frac{\sin \left( m - n \right)x}{m - n} \right] + C\]
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