Question

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

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:

\(0\)