## anonymous 5 years ago Use identities (no calculators) to find the exact value for (sin 38)(sin 112) -( cos 38)(cos 112).

1. anonymous

same trick as before. this is the addition angle formula for cosine{ $cos(a+b)=cos(a)cos(b)-sin(a)sin(b)$

2. anonymous

here $a=38,b=112, a+b=150$

3. anonymous

well on careful inspection i see that this is it's negative, but that is ok $cos(150)=-\frac{\sqrt{3}}{2}$ so your answer here is $\frac{\sqrt{3}}{2}$

4. anonymous

Why does the negative turn to a positive?

5. anonymous

oh because the "addition angle" formula is not the one written in the question. it is its negative