Answer:
[tex]-\sqrt{3} /2[/tex]
Step-by-step explanation:
Note that this looks like the identity:
cos(A + B) = cosAcosB - sinAsinB.
In this case, A = π/12 and B = 3π/4. So, we can say that the given equation:
cos(π/12)cos(3π/4) - sin(π/12)sin(3π/4) = cos(π/12 + 3π/4) = cos(π/12 + 9π/12) = cos(10π/12) = cos(5π/6)
Ah, now we have a trigonometry problem we can easily solve!
cos(5π/6) = -cos(π/6) = -(√3)/2
Hope this helps!
