13. Find the general solution of the equation (sin 2x -sin 4x + sin 6x

1.	13. Find the general solution of the equation (sin 2x -sin 4x + sin 6x-0)
Answer» Here is the solution to your answer: Given: sin2x + sin 4x + sin6x=0 (sin 2x + sin 6x) + sin 4x = 0 2.sin[ (2x+6x)/2 ].cos[ (2x-6x)/2 ] + sin 4x = 0 2sin4x.cos2x + sin 4x = 0 sin 4x (2cos 2x +1) = 0 sin 4x = 0 ............... or.............. 2cos2x + 1 = 0 4x = n(pi) ................or .............. cos2x = -1/2 x = [ n(pi)/4 ].............or ............. cos 2x = cos [ 2(pi)/3 ] ................. 2x = 2n(pi) +/- [ 2(pi)/3 ] .................x = n(pi) +/- [ (pi)/3 ] >>>>>>>>>>> " +/- " means "plus or minus" thnku

13. Find the general solution of the equation (sin 2x -sin 4x + sin 6x-0)

Answer»

Here is the solution to your answer:

Given:

sin2x + sin 4x + sin6x=0

(sin 2x + sin 6x) + sin 4x = 0

2.sin[ (2x+6x)/2 ].cos[ (2x-6x)/2 ] + sin 4x = 0

2sin4x.cos2x + sin 4x = 0

sin 4x (2cos 2x +1) = 0

sin 4x = 0 ............... or.............. 2cos2x + 1 = 0

4x = n(pi) ................or .............. cos2x = -1/2

x = [ n(pi)/4 ].............or ............. cos 2x = cos [ 2(pi)/3 ]

................. 2x = 2n(pi) +/- [ 2(pi)/3 ]

.................x = n(pi) +/- [ (pi)/3 ] >>>>>>>>>>> " +/- " means "plus or minus"

thnku