SOLUTION: Can you Proof the following Identity? CosA cos(-A)- sinAsin(-A)=1

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Question 747302: Can you Proof the following Identity?
CosA cos(-A)- sinAsin(-A)=1
Found 2 solutions by tommyt3rd, josgarithmetic:
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
in the equation
%0D%0Acos%28A%29+cos%28-A%29-+sin%28A%29sin%28-A%29=1%0D%0A
we notice the evenness and oddness of cosine and sine:
%0D%0Acos%28-theta%29=cos%28theta%29%0D%0A
and
%0D%0Asin%28-theta%29=-sin%28theta%29%0D%0A
therefore...
%0D%0Acos%28A%29+cos%28-A%29-+sin%28A%29sin%28-A%29=cos%5E2%28A%29%2Bsin%5E2%28A%29=1%0D%0A

:)

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Using symmetry of the functions, cos%28A%29=cos%28-A%29, and sin%28-A%29=-sin%28A%29. Check on the Unit Circle to be sure this makes sense.

Those facts let us say this step.

=cos%28A%29cos%28A%29-%28-1%29sin%28A%29%2Asin%28A%29
=%28cos%28A%29%29%5E2%2B%28sin%28A%29%29%5E2=1
DONE.