This equation can be simplified using trigonometric identities.
Expanding the left side of the equation:cosx = (cos(x/2) - sin(x/2))^2 - 1cosx = cos^2(x/2) - 2cos(x/2)sin(x/2) + sin^2(x/2) - 1cosx = cos^2(x/2) - 2cos(x/2)sin(x/2) + sin^2(x/2) - cos^2(π/2)cosx = cos^2(x/2) - 2cos(x/2)sin(x/2) + sin^2(x/2) - sin^2(π/2)cosx = cos^2(x/2) - 2cos(x/2)sin(x/2) + sin^2(x/2) - 1
So the simplified equation is:cosx = cos^2(x/2) - 2cos(x/2)sin(x/2) + sin^2(x/2) - 1
This equation can be simplified using trigonometric identities.
Expanding the left side of the equation:
cosx = (cos(x/2) - sin(x/2))^2 - 1
cosx = cos^2(x/2) - 2cos(x/2)sin(x/2) + sin^2(x/2) - 1
cosx = cos^2(x/2) - 2cos(x/2)sin(x/2) + sin^2(x/2) - cos^2(π/2)
cosx = cos^2(x/2) - 2cos(x/2)sin(x/2) + sin^2(x/2) - sin^2(π/2)
cosx = cos^2(x/2) - 2cos(x/2)sin(x/2) + sin^2(x/2) - 1
So the simplified equation is:
cosx = cos^2(x/2) - 2cos(x/2)sin(x/2) + sin^2(x/2) - 1