Your use of parentheses is not standard, so I made a guess as to the equation in this exercise.
1 - 2*sin(x)^2 + sin(4x) = 3*cos(x)^2 - 3*sin(x)^2
No, this is not an identity.
Look at two of the double-angle identities for cosine:
cos(x)^2 - sin(x)^2 = cos(2x)
1 - 2*sin(x)^2 = cos(2x)
What do you get, after making these two substitutions in your equation and simplifying?