The constant from part (i) is found by setting $x=0$:
$$
F(0)=s(a).
$$
Taking $a=x+y$ therefore gives the <sine addition formula>
$$
\boxed{s(x+y)=s(x)c(y)+c(x)s(y)}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2020 / ia / Paper 1 / 9D / b / ii / Solution

{title2=$\sin(x+y)=\sin x\cos y+\cos x\sin y$}


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