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

Ah my bad, but I know the formulas but I don't see how to convert this:

Edit: Oh ok I see how to convert the first one now, but the second one confuses me on how to convert this:

3. (fill in the values) -sqrt(3) - 1 / 1 (-sqrt(3)) x 1

to this:

4. (Final answer) 2 [plus] sqrt(3)

Uhh, formulas are hard to read but if that is  1/4*(sqrt(2) sqrt(6))  then it's automatically 1/4*sqrt(2) 1/4*sqrt(6) simply through expansion.

I edited the post quickly after I posted that and I figured it out, but the second problem still puzzles me.

Kind of hard to read but you just simplify from step 3 to 4.

For example, in ex1 you would multiply step 3 out. in step 4 you factored out the 1/4.

Same thing with ex2. you simplyfy it to get step 4

Man, you just reminded me how much I hate mathematics. The only thing I remember about trigonometry is that:

Cos 90 = Sin 0 = srt 0 / 2

Cos 60 = Sin 30 = srt 1 / 2

Cos 45 = Sin 45 = srt 2 / 2

Cos 30 = Sin 60 = srt 3/ 2

Cos 0 = Sin 90 = srt 4 / 2

Kinda easy way to memorize it, eh?

Ok second one

Tan(75) = (Tan(120)-Tan(45))/(1 [plus] tan(120)*tan(45))

Is the formula you should be using.

For problem #2, you have to use this identity: Tan{X( /-)Y]= [Tan[X]( /-)Tan[Y]} / {1(-/ )Tan[X]Tan[Y]}

The /- indicates whether or not you are adding or subtracting.  The next /- is written in the same way, so you will use the same symbol, however, the final one is written as -/ , which indicates you will do the opposite of what you did for the first two.

So you have: Tan (120-45)= [Tan (120) - Tan (45)] / [1 Tan (120) Tan (45)]

You can simplify this to the following: [-sqrt(3) - 1] / [1 - sqrt(3)]

In order to simplify that, you have to multiply both the top and the bottom by: [1 sqrt(3)], which is simply the bottom function with its sign changed.

When you do this, you will get: [-2sqrt(3) - 4] / (-2)

All values are negatives, so you can get rid of the minus signs.  You then need to divide both the top values by 2 so you won't have a denominator, which results in: sqrt(3) 2

Hope that helps :D

Sweet thanks for the help guys. For some reason I just couldn't figure out the way to simplify it.