Sin 3x + COS 3x=0

To solve the equation sin(3x) + cos(3x) = 0, we can use the trigonometric identity:

sin(a) + cos(a) = √2 sin(a + π/4)

Now, let's rewrite the equation:

sin(3x) + cos(3x) = √2 sin(3x + π/4)

For sin(3x + π/4) = 0, we have:

3x + π/4 = kπ, where k is an integer

Now solve for x:

3x = kπ - π/4

x = (kπ - π/4) / 3

Therefore, the general solution for the equation sin(3x) + cos(3x) = 0 is:

x = (kπ - π/4) / 3, where k is an integer