Match each expression with its product-to-sum formula. (a) sin(u)cos(v) (1)/(2)[sin(u+v)+sin(u-v)] (1)/(2)[sin(u+v)-sin(u-v)] (b) cos(u)sin(v) (1)/(2)[cos(u-v)+cos(u+v)] (1)/(2)[sin(u+v)+sin(u-v)] (1)/(2)[sin(u+v)-sin(u-v)] (c) cos(u)cos(v) (1)/(2)[cos(u-v)+cos(u+v)] (1)/(2)[sin(u+v)+sin(u-v)] (1)/(2)[sin(u+v)-sin(u-v)]

Let's match each expression with its corresponding product-to-sum formula:<br /><br />(a) $sin(u)cos(v)$<br />The correct formula is:<br />$\frac {1}{2}[sin(u+v)+sin(u-v)]$<br /><br />(b) $cos(u)sin(v)$<br />The correct formula is:<br />$\frac {1}{2}[sin(u+v)-sin(u-v)]$<br /><br />(c) $cos(u)cos(v)$<br />The correct formula is:<br />$\frac {1}{2}[cos(u-v)+cos(u+v)]$<br /><br />So the matches are:<br />(a) $sin(u)cos(v)$ with $\frac {1}{2}[sin(u+v)+sin(u-v)]$<br />(b) $cos(u)sin(v)$ with $\frac {1}{2}[sin(u+v)-sin(u-v)]$<br />(c) $cos(u)cos(v)$ with $\frac {1}{2}[cos(u-v)+cos(u+v)]$