Cosx=(cos(x/2)-sin(x/2))^2-1

Предыдущий
вопрос Следующий
вопрос

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