Need some help with trigonometry related questions

[trestres]

AdventWolf said:

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.

The first one uses the trigonometric identity that

sin(a b) = sin(a) x cos( b ) cos(a) x sin( b )


The second one you wrote it incorrectly, it's supposed to be tan 75° = tan (120°- 45°), and not tan 75° = tan 120° - tan 45° because that's not true.

Anyways use this identity tan(a - b) = (tan (a) x tan (b)) / (1 (tan (a) x tan ( b ))


They are just mathematical identities, which means that you can write the same thing in a different way.

Plus sign doesnt work, here have this link http://www.math.com/tables/trig/identities.htm