Question

Tentukan solusinya :
1. sin x + sin 2x = 0
2. cos 2x + cos 4x = 0
3. tan x + tan 3x = 0

Answer 1

1.2 cos x = 1 
cos x = 1/2 
 x = ±π/3 + 2πn

2.cos(2x) + cos(4x) = 0 
cos(3x-x) + cos(3x+x) = 0 
cos(3x)cos(x) + sin(3x)sin(x) + cos(3x)cos(x) - sin(3x)sin(x) = 0 
2cos(3x)cos(x) = 0 
cos(3x)cos(x) = 0 

cos(3x) = 0 
3x = {π/2, 3π/2, 5π/2. 7π/2, 9π/2. 11π/2} 
x = {π/6, π/2, 5π/6. 7π/6, 3π/2. 11π/6} 

cos(x) = 0 
x = {π/2, 3π/2} 

x = {π/6, π/2, 5π/6. 7π/6, 3π/2. 11π/6}

3.tan(3x) = 0, tan x = 1 
3x = 0,pi,2pi..x = pi/4, 5pi/4 
x = 0,pi/4,pi,5pi/4,2pi