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

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

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

Answer

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)