Alright so I have a couple of problems that I am looking over and they use the sum and difference formulas. I get lost on the last step where they somehow convert an equation into a totally different answer and for some reason I don't see how it's done and the book skips straight to the answer.
Ex 1 (sum formula)
Find: sin 7pi/12
1. sin 7pi / 12 = sin(3pi/12 + 4pi/12) = sin(pi/4 + pi/3)
2. (fill in formula) sin pi/4 x cos pi/3 + cos pi/4 x sin pi/3
3. (fill in values) sqrt(2)/2 x 1/2 + sqrt(2)/2 x sqrt(3)/2
4. (Final answer) 1/4(sqrt(2) + sqrt(6)
Ex 2(difference formula)
Find: Tan 75*
1. tan 75* = tan 120* - tan 45*
2. (Fill in formula) tan 120* - tan 45* / 1 + tan 12-* X tan 45*
3. (fill in the values) -sqrt(3) - 1 / 1 + (-sqrt(3)) x 1
4. (Final answer) 2 + sqrt(3)
Basically I just need help figuring out how they go from step 3 to step 4. Thanks for any help you can give.
