is in quadrant I, so
.
is in quadrant II, so
.
Recall that for any angle
,

Then with the conditions determined above, we get

and

Now recall the compound angle formulas:




as well as the definition of tangent:

Then
1. 
2. 
3. 
4. 
5. 
6. 
7. A bit more work required here. Recall the half-angle identities:



Because
is in quadrant II, we know that
is in quadrant I. Specifically, we know
, so
. In this quadrant, we have
, so

8. 
The answer is -8 because -2 * 4
Depends on what the measurement is.
see attached picture for #6
10 the inequality would be :
12 inch box is x
15 inch box is y
12x+15y≤84