This expression can be written as:
2cos^2(x)cos(x) - sin(x)*sin(2x)
Using trigonometric identities, we can simplify this expression further:
cos(2x) = 2cos^2(x) - 1sin(2x) = 2sin(x)*cos(x)
Now substituting these identities into the expression, we get:
2(2cos^2(x) - 1)cos(x) - sin(x)(2sin(x)cos(x))= 4cos^3(x) - 2cos(x) - 2sin^2(x)cos(x)= 4cos^3(x) - 2cos(x) - 2(1 - cos^2(x))cos(x)= 4cos^3(x) - 2cos(x) - 2cos(x) + 2cos^3(x)= 6cos^3(x) - 4cos(x)
Therefore, the simplified expression is 6cos^3(x) - 4cos(x).
This expression can be written as:
2cos^2(x)cos(x) - sin(x)*sin(2x)
Using trigonometric identities, we can simplify this expression further:
cos(2x) = 2cos^2(x) - 1
sin(2x) = 2sin(x)*cos(x)
Now substituting these identities into the expression, we get:
2(2cos^2(x) - 1)cos(x) - sin(x)(2sin(x)cos(x))
= 4cos^3(x) - 2cos(x) - 2sin^2(x)cos(x)
= 4cos^3(x) - 2cos(x) - 2(1 - cos^2(x))cos(x)
= 4cos^3(x) - 2cos(x) - 2cos(x) + 2cos^3(x)
= 6cos^3(x) - 4cos(x)
Therefore, the simplified expression is 6cos^3(x) - 4cos(x).