Question

Sin^2 x/2+cos^2 x/2=cosx

Answer 1

1/2sin^2x+1/2cos^2=cosx
1/2(sin^2x+cos^2x)=cosx
1/2=cosx
x=Π/3

Answer 2

The identity you've written is not correct. The identity you are likely trying to use is the double angle identity for cosine, which states:

cos(2x) = cos^2(x) - sin^2(x)

If we divide both sides of this identity by 2, we get:

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

So, the correct identity is:

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

Your equation:

sin^2(x/2) + cos^2(x/2) = cos(x)

Is not a valid trigonometric identity or equation. It doesn't follow from the standard trigonometric identities, and it's not true for all values of x.