Answer:
see below
Step-by-step explanation:
The double angle formulas for trig functions are generally based on the sum of angle formulas, where the two angles are equal.
cos(a+b) = cos(a)cos(b) -sin(a)sin(b)
When a=b=x, then ...
cos(2x) = cos(x)² -sin(x)²
The Pythagorean identity can be used to substitute for either of the squares:
cos(2x) = (1 -sin(x)²) -sin(x)²
cos(2x) = 1 - 2sin(x)²
or
cos(2x) = cos(x)² -(1 -cos(x)²)
cos(2x) = 2cos(x)² - 1
