Question

write the expression as the sine or cosine of an angle.
cos 7y cos 3y − sin 7y sin 3y
?( y)
hint: sin(a ± b) = sin a cos b ± cos a sin b
cos(a ± b) = cos a cos b ∓ sin a sin b

Explanation:

Step1: Recall the cosine addition formula

The formula for the cosine of a sum of two angles is $\cos(A + B) = \cos A \cos B - \sin A \sin B$.

Step2: Identify A and B in the given expression

In the expression $\cos 7y \cos 3y - \sin 7y \sin 3y$, we can see that $A = 7y$ and $B = 3y$.

Step3: Apply the formula

Substituting $A = 7y$ and $B = 3y$ into the formula $\cos(A + B) = \cos A \cos B - \sin A \sin B$, we get $\cos(7y + 3y)=\cos(10y)$.

Answer:

$\cos(10y)$ (So the first box is $\cos$ and the second box is $10$)