Question

Use identities (no calculators) to find the exact value for (sin 38)(sin 112) -( cos 38)(cos 112).

Answer 1

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

Answer 2

here \[a=38,b=112, a+b=150\]

Answer 3

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
\[\frac{\sqrt{3}}{2}\]

Answer 4

Why does the negative turn to a positive?

Answer 5

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