SOLUTION: cos(-x)cos x - sin (-x) sin x

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Question 1027182: cos(-x)cos x - sin (-x) sin x
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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cos(-x)*cos(x) - sin(-x)*sin(x)
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One way to find its value is

cos(-x)*cos(x) - sin(-x)*sin(x) = cos%5E2%28x%29+%2B+sin%5E2%28x%29 = 1.

(On the way I used  cos(-x) = cos(x)  and  sin(-x) = -sin(x)).



The other way is to use the addition formula of trigonometry for cosines,
which is  cos%28alpha%29%2Acos%28beta%29+-+sin%28alpha%29%2Asin%28beta%29 = cos%28alpha+%2B+beta%29.


When you use it with alpha = -x  and  beta = x,  you will get

cos(-x)*cos(x) - sin(-x)*sin(x) = cos((-x) + x) = cos(0) = 1.


Both ways lead to the same result.