2. Find the general solution of sin 2r + sin 4x +sin 6r- 0.

1.	2. Find the general solution of sin 2r + sin 4x +sin 6r- 0.
Answer» Using, sin(C) + sin(D) = 2[sin{(C + D)/2}cos{(C-D)/2}], sin(6x) + sin(2x) = 2sin(4x)cos(2x) 2) HENCE, sin(2x)+sin(4x)+sin(6x)=0, ==> 2sin(4x)*cos(2x) + sin(4x) = 0 3) ==> sin(4x){1 + 2cos(2x)} = 0 4) ==> Either sin(4x) = 0 or 1 + 2cos(2x) = 0 5) When sin(4x) = 0, the general solution for 4x = 2kπ, where 'k' is an integerSo, 'x' = kπ/2 6) When 1 + 2cos(2x) = 0, cos(2x) = -1/2 ==> the general solution for 'x' = (2k + 1)(π/2) ± (π/6)

Answer»

Using, sin(C) + sin(D) = 2[sin{(C + D)/2}*cos{(C-D)/2}],

sin(6x) + sin(2x) = 2sin(4x)*cos(2x)

2) HENCE, sin(2x)+sin(4x)+sin(6x)=0, ==> 2sin(4x)*cos(2x) + sin(4x) = 0

3) ==> sin(4x){1 + 2cos(2x)} = 0

4) ==> Either sin(4x) = 0 or 1 + 2cos(2x) = 0

5) When sin(4x) = 0, the general solution for 4x = 2kπ, where 'k' is an integerSo, 'x' = kπ/2

6) When 1 + 2cos(2x) = 0, cos(2x) = -1/2

==> the general solution for 'x' = (2k + 1)(π/2) ± (π/6)

Discussion