To solve this equation, we'll move all the terms to the
left side:
cos 4x - cos 2x =
0
Since the trigonometric functions are matching , we'll
transform the difference into a product.
2
sin[(4x+2x)/2]*sin [(2x-4x)/2]=0
2 sin3x* sin
(-x)=0
From this product of 2 factors, one or the other
factor is zero.
sin3x=0
This
is an elementary equation:
3x = (-1)^k*arcsin 0 +
k*pi
3x = k*pi
x = k*pi/3,
where k is an integer number.
We'll solve the second
elementary equation:
sin
(-x)=0
-sin (x)=0
sin
x=0
x=(-1)^k arcsin 0 +
k*pi
x=k*pi
The
set of solutions is : S={k*pi/3}U{k*pi}.
No comments:
Post a Comment