Question 428624
(1 + cos) * (1 - cos) should result in:


1^2 - cos + cos - cos^2 which should result in 1^2 - cos^2 which should result in 1 - cos^2.


from the pythagorean theorem, we get sin^2 + cos^2 = 1 (theta, or the angle in question, is implied).


if we subtract cos^2 from both sides of this equation, we get 1 - cos^2 = sin^2


so what resulted in 1 - cos^2 should be equivalent to sin^2 which yields to the conclusion that:


(1 + cos) * (1 - cos) = sin^2


let's see if this holds water.


assume our angle is 30 degrees.


(1 + cos(30)) * (1 - cos(30)) will be equal to .25


sin (30) = .5


sin^2 (30) = .5^2 = .25


looks like it works !!!!!


let's try another angle at random.


let's try an angle of 53 degrees

(1 - cos(53)) * (1 + cos(53) = .637818678


sin(53) = .79863551


sin^2(53) = .79863551^2 = .637818678


it works again !!!!!


the answer to your question i that, yes, algebraically, this kind of looks like the difference of square, i.e. (x-a) * (x+a) = x^2 - a^2.


the operation is similar.


the translation, however, does depend on knowledge of the pythagorean formula of sin^2 + cos^2 = 1 in order to get the final answer.