given: a. sin(x) b. cos(x) c. cos(y) d. sin(y) use the drop - down menus in the derivation of the cosine sum…

Explanation:

Step1: Recall cosine - difference identity

The cosine - difference identity is $\cos(A - B)=\cos A\cos B+\sin A\sin B$. Here $A=\frac{\pi}{2}-x$ and $B = y$. So $\cos((\frac{\pi}{2}-x)-y)=\cos(\frac{\pi}{2}-x)\cos y+\sin(\frac{\pi}{2}-x)\sin y$.

Step2: Use co - function identities

We know that $\cos(\frac{\pi}{2}-x)=\sin x$ and $\sin(\frac{\pi}{2}-x)=\cos x$. Substituting these into the above expression, we get $\sin x\cos y+\cos x\sin y$.

Answer:

The first blank should be filled with $\cos(y)$ and the second blank should be filled with $\sin(y)$. So the answers are C and D.