Draw a right triangle with angle x, hypotenuse 1, and legs "a" and "b"
Since
, that's
because by the Pythagorean theorem, a2+b2=1
Multiply top and bottom by a2b2
We multiply out the denominator,
Since a2+b2=1,
The denominator factors
Multiply by the product of the "conjugates" of the
factors on the bottom over itself. (Sort of like
rationalizing the denominator)


By the Pythagorean theorem 1-a2=b2 and 1-b2=a2
Canceling:
Since a = sin(x) and b = cos(x)
<--simplest form
Edwin