Question

` ∫    cos  mx  cos  nx  dx `

 

Answer 1

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