Question

Find the general solution for x in :
sin mx + sin nx = 0​

Answer 1

Answer:

$x \: = 2p\pi \div ( \: m \: + n \: )$

$and$

$x \: = (2q \: + 1)\pi \div (m - n)$

Step-by-step explanation:

Given ,

=) Sin mx + Sin nx = 0

=) 2Sin [ ( mx + nx ) / 2] * Cos [ ( mx - nx ) / 2 ] = 0

Case 1

=) Sin [ ( mx + nx ) / 2 ] = 0

=) ( mx + nx ) / 2 = pπ ( where p is an integer )

=) x = 2pπ / ( m + n )

Case II

=) Cos [ ( mx– nx ) / 2 ] = 0

=) ( mx – nx ) / 2 = ( 2q + 1 ) π / 2 ( where q is an integer )

=) x = ( 2q + 1 ) π / ( m – n ) .