# Cos75Cos15-sin75sin15

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### 3 Answers

We know that cosAcosB-sinAsinB=cos(A+B)

cos75.cos15-sin75.sin15=cos(75+15)

=cos90 (If The angle given is in degree)

=0

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.

note:

cos(x)*cos(y) = 1/2 (cos(x-y)+cos(x+y))and

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:

=(1/4)-(1/4)

=0

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