To solve this equation, we can use the trigonometric identity:
cos(a) = cos(b) if and only if a = 2nπ ± bwhere n is an integer.
So, we have:
3x - π/6 = x + π/4
Subtract x from both sides:
2x - π/6 = π/4
Add π/6 to both sides:
2x = π/4 + π/62x = 3π/12 + 2π/122x = 5π/12
Divide by 2:
x = 5π/24
Therefore, the solution to the equation is x = 5π/24.
To solve this equation, we can use the trigonometric identity:
cos(a) = cos(b) if and only if a = 2nπ ± b
where n is an integer.
So, we have:
3x - π/6 = x + π/4
Subtract x from both sides:
2x - π/6 = π/4
Add π/6 to both sides:
2x = π/4 + π/6
2x = 3π/12 + 2π/12
2x = 5π/12
Divide by 2:
x = 5π/24
Therefore, the solution to the equation is x = 5π/24.