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Im not sure about your question here. If you need to simplify, you can just use your calculator and input cos(75)cos(15)-sin(75)sin(15) and press =.
You will be getting zero (0).
There is and identity for `cos(75)cos(15)-sin(75)sin(15)` .
Recall `cos(A+B) = cosAcosB - sinAsinB.`
Simply, A = 75 and B = 15.
So cos(75+15) = cos(90) = 0.
Therefore, the answer is 0.
We know that cosAcosB-sinAsinB=cos(A+B)
=cos90 (If The angle given is in degree)
note:cos(x)*cos(y) = 1/2 (cos(x-y)+cos(x+y))
sin(x)sin(y) = 1/2 (cos(x-y)-cos(x+y))
therefor: 1/2 (cos(x-y)-cos(x+y)) - 1/2 (cos(x-y)-cos(x+y)) = 0
if you punch it into a calculator you get:
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