Question

What is the value of $\cos ({30}^0+x)\cos ({30}^0-x)-\sin ({30}^0-x)$?

Answer 1

Since $\cos A\cos B-\sin A\sin B=\cos (A+B)$
$\therefore$ The given expression has the value
$=\cos ({30}^0+x+{30}^0-x)=\cos {60}^0=\frac{1}{2}$