Question

write the expression as the sine or cosine of an angle.\
\cos 7y\cos 3y - \sin 7y\sin 3y\
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hint: \sin (a \pm b)=\sin a\cos b \pm \cos a\sin b\
\cos (a \pm b)=\cos a\cos b \mp \sin a\sin b

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, \(A = 7y\) and \(B=3y\).

Step3: Apply the formula

Substitute \(A = 7y\) and \(B = 3y\) into the formula \(\cos(A + B)\). So, \(\cos7y\cos3y-\sin7y\sin3y=\cos(7y + 3y)\)

Answer:

\(\cos(10y)\)