Answer
$$\cos74^\circ=\cos60^\circ\cos14^\circ+\sin60^\circ\sin14^\circ$$
The statement is false.
Work Step by Step
$$\cos74^\circ=\cos60^\circ\cos14^\circ+\sin60^\circ\sin14^\circ$$
As $74^\circ=60^\circ+14^\circ$,
$$\cos74^\circ=\cos(60^\circ+14^\circ)$$
Now we use the cosine sum identity:
$$\cos(A+B)=\cos A\cos B-\sin A\sin B$$ (be extremely careful about the sign in the middle)
That means
$$\cos74^\circ=\cos60^\circ\cos14^\circ-\sin60^\circ\sin14^\circ$$
As you see, the sign in the middle is different:
$$\cos60^\circ\cos14^\circ-\sin60^\circ\sin14^\circ\ne\cos60^\circ\cos14^\circ+\sin60^\circ\sin14^\circ$$
Therefore, the statement
$$\cos74^\circ=\cos60^\circ\cos14^\circ+\sin60^\circ\sin14^\circ$$
is false.
