Question

Integrate the integral: ∫cos mx cos nx dx, m ≠ n

Answer 1

Given as ∫cos mx cos nx dx, m ≠ n

As we know that 2cos A cos B = cos (A - B) + coa (A + B)

On substituting the above formula, we get

So, cos mx cos nx = (cos(m - n)x + cos (m + n)x)/2

So, the equation becomes,

As we know that a² - b² = (a + b) (a - b)

On substituting the above formula and satisfying, we get