simplify the expression by using an appropriate identity. do not use a calculator. (cos 22°)(cos 68°)-(sin…

Explanation:

Step1: Recall the cosine addition formula

The formula for (\cos(A + B)=\cos A\cos B-\sin A\sin B).

Step2: Identify (A) and (B)

Let (A = 22^{\circ}) and (B=68^{\circ}). Then the given expression ((\cos22^{\circ})(\cos68^{\circ})-(\sin22^{\circ})(\sin68^{\circ})) is in the form of (\cos(A + B)).

Step3: Calculate (A + B)

(A + B=22^{\circ}+68^{\circ}=90^{\circ}).

Step4: Evaluate (\cos(A + B))

Since (\cos90^{\circ}=0).

Answer:

(0)