Please show your work thanks Find the exact value of the tri

Please show your work, thanks!

Find the exact value of the trig expression without using a calculator: cos(7pi/12)*cos(5pi/12) - sin(7pi/12)*sin(5pi/12).

Solution

cos(7pi/12)cos(5pi/12)-sin(7pi/12)sin(5pi/12)

This is of the form

cos A cos B - sin A sin B= cos(A+B

So we get

cos(7pi/12 + 5pi/12)= cos 12pi/12=cos pi =-1