Question

solve the equation sin mx+sin nx=0

Answer 1

Given:

The equation sin mx + sin nx = 0

To find:

Solve the equation sin mx + sin nx = 0

Solution:

From given, we have,

The equation sin mx + sin nx = 0

use the formula,

sin a + sin b = 2 sin (a+b)/2 cos (a-b)/2

2 sin (m+n)x/2 cos (m-n)x/2 = 0

sin (m+n)x/2 cos (m-n)x/2 = 0

sin (m+n)x/2  = 0

and

cos (m-n)x/2 = 0

sin (m+n)x/2  = 0

(m+n)x/2  =px

cos (m-n)x/2 = 0

(m-n)x/2 = (2q + 1)x/2

p, q ∈ I

x = 2px/(m + n)

x = (2q + 1)x/(m - n)

Therefore, the solution of the equation sin mx + sin nx = 0 is x = 2px/(m + n) and x = (2q + 1)x/(m - n)