Question

simplify the expression by using an appropriate identity. do not use a calculator. (cos 66°)(cos 24°)-(sin 66°)(sin 24°) (cos 66°)(cos 24°)-(sin 66°)(sin 24°)=\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 \(B\)

Here \(A = 66^{\circ}\) and \(B=24^{\circ}\).
So \(\cos66^{\circ}\cos24^{\circ}-\sin66^{\circ}\sin24^{\circ}=\cos(66^{\circ}+ 24^{\circ})\).

Step3: Calculate the sum

\(66^{\circ}+24^{\circ}=90^{\circ}\).
So \(\cos(66^{\circ}+24^{\circ})=\cos90^{\circ}\).

Step4: Evaluate \(\cos90^{\circ}\)

We know that \(\cos90^{\circ}=0\).

Answer:

\(0\)