Expressing trig functions as one angle

[kelleynicole30]

Express as a trigonometric function of one angle.

1) cos3 sin(-2)-cos2sin3

2) sin(-5)cos2+cos5sin(-2)

I know that the add/sub formulas are used in finding the answer but I can't figure out how to reverse the order to solve it and match the formulas. I'm getting very confused with the negatives in the questions. Help would be apprecitated.

 

[soroban]

Hello, kelleynicole30!

We're expected to know that: .\(\displaystyle \sin(-\theta) \:=\:-\sin\theta\)

Express as a trigonometric function of one angle.

\(\displaystyle 1)\;\;\cos(3)\sin(-2) - \cos(2)\sin(3)\)

\(\displaystyle \text{We have: }\;-\sin(2)\cos(3) - \sin(3)\cos(2)\)

\(\displaystyle \text{Factor: }\;-\bigg[\sin(2)\cos(3) + \sin(3)\cos(2)\bigg]\)

\(\displaystyle \text{And we have: }\;-\sin(2+3) \;=\;-\sin(5)\)

\(\displaystyle 2)\;\;\sin(-5)\cos(2)+\cos(5)\sin(-2)\)

\(\displaystyle \text{We have: }\;-\sin(5)\cos(2) - \sin(2)\cos(5)\)

\(\displaystyle \text{Factor: }\;-\bigg[\sin(5)\cos(2) + \sin(2)\cos(5)\bigg]\)

\(\displaystyle \text{And we have: }\;-\sin(5+2) \;=\;-\sin(7)\)