To solve this equation, we can expand the left side and simplify.
(Sin x/2 - cos x/2)^2= (sin^2(x/2) - 2sin(x/2)cos(x/2) + cos^2(x/2))= sin^2(x/2) + cos^2(x/2) - 2sin(x/2)cos(x/2)= 1 - 2sin(x/2)cos(x/2)
Now we have:
1 - 2sin(x/2)cos(x/2) = -1/2
Multiplying by 2 to get rid of the fraction:
2 - 4sin(x/2)cos(x/2) = -1
Rearranging:
4sin(x/2)cos(x/2) = 3
sin(x) = 2(2sin(x/2)cos(x/2))
Using the double angle formula for sine:
sin(x) = 2sin(x/2)cos(x/2)
Since sin(x) = 2sin(x/2)cos(x/2), we see that sin(x) = sin(x). Therefore, this equation holds true for all values of x.
To solve this equation, we can expand the left side and simplify.
(Sin x/2 - cos x/2)^2
= (sin^2(x/2) - 2sin(x/2)cos(x/2) + cos^2(x/2))
= sin^2(x/2) + cos^2(x/2) - 2sin(x/2)cos(x/2)
= 1 - 2sin(x/2)cos(x/2)
Now we have:
1 - 2sin(x/2)cos(x/2) = -1/2
Multiplying by 2 to get rid of the fraction:
2 - 4sin(x/2)cos(x/2) = -1
Rearranging:
4sin(x/2)cos(x/2) = 3
sin(x) = 2(2sin(x/2)cos(x/2))
Using the double angle formula for sine:
sin(x) = 2sin(x/2)cos(x/2)
Since sin(x) = 2sin(x/2)cos(x/2), we see that sin(x) = sin(x). Therefore, this equation holds true for all values of x.