This is not a true statement. The given equation sin(x)^4 + cos(x)^4 = sin(x)cos(x) is not true for all values of x.
For example, if we take x = π/4, then the left side of the equation would be sin(π/4)^4 + cos(π/4)^4 = (sqrt(2)/2)^4 + (sqrt(2)/2)^4 = 1/4 + 1/4 = 1/2.
On the other hand, the right side of the equation would be sin(π/4)cos(π/4) = (sqrt(2)/2)*(sqrt(2)/2) = 1/2.
Therefore, the given equation is true for some values of x, but not for all values of x.
This is not a true statement. The given equation sin(x)^4 + cos(x)^4 = sin(x)cos(x) is not true for all values of x.
For example, if we take x = π/4, then the left side of the equation would be sin(π/4)^4 + cos(π/4)^4 = (sqrt(2)/2)^4 + (sqrt(2)/2)^4 = 1/4 + 1/4 = 1/2.
On the other hand, the right side of the equation would be sin(π/4)cos(π/4) = (sqrt(2)/2)*(sqrt(2)/2) = 1/2.
Therefore, the given equation is true for some values of x, but not for all values of x.