#1-10. In each case, we need to find a way to add or subtract our common angles so they equal the angle in question. For example, if we want to equal 15o, probably the easiest way is to use 45o - 30o = 15o. Then we will use one of the difference of angles formulas to find trig(15o). For another example, observe that 11π/12 = 8π/12 + 3π/12 = 2π/3 + π/4. Those last two angles are two of our special angles.
#11-16. Look at the expression, and compare it to the sum or difference of angles formulas. Which one does it match up with? What would A & B have to be? And then what does the other side of the formula tell you this must equal. For example, if we need to find sin(18o)cos(27o)+cos(18o)sin(27o), observe that this matches up with sin(A)cos(B) + cos(A)sin(B), which is the formula for sin(A+B). In this case, A=18o and B=27o, so A+B = 45o, so our expresion equals sin(45o), which equals ???.
#21-38. In each case, we need to verify the identity. That is, we need to manipulate one side of the equation to make it look like the other side. (Or we could manipulate both sides to meet somewhere in the middle.) Remember that one of our strategies was to get a common argument. In most (all?) of these problems you will need to use a sum or difference of angles formula to "break up" an argument or two. For example, on #27, we need to use a sum of angles formula on cos(x+π/6) and a difference of angles formula on sin(x-π/3).
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