How sin^2( x/2)=(1-cosx)/2 only 2 is the power of sin and 2 comes under 1-cosx? How it ====》 sin^2 x=(1-cos2x) /2 how 2 which was under x goes with cos but not goes with 1 like (2-cos2x)/2
What you have here is an identity. An identity is an expression which is true for all values of x.
For example, sin^2(x) + cos^2(x) = 1.
That is an identity, and is true no matter what value x has.
Another trig identity is, cos(2A) = cos^2(A) – sin^2(A)
We can manipulate this as follows.
cos(2A) = cos^2(A) – sin^2(A)
cos(2A) = (1 – sin^2(A)) – sin^2(A)
cos(2A) = 1 – 2sin^2(A)
Rearranging,
2sin^2(A) = 1 – cos(2A)
sin^2(A) = (1/2)(1 – cos(2A))
Now let A = x/2. Then,
sin^2(x/2) = (1 – cos(x))/2