Question 1027182
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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^2(x) + sin^2(x)}}} = 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(alpha)*cos(beta) - sin(alpha)*sin(beta)}}} = {{{cos(alpha + beta)}}}.


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.
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