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# Core 3 trigonometry watch

1. I need to use the identity:

sin(A + B) - sin(A - B)/cos(A - B) - cos(A + B) = cotA

along with the exact values of cos 60 and sin 60 to find an exact value for cot 75 in its simplest form. I'm not sure what to do, though.
2. Could you post the actual question please?
It would be a lot easier to understand.
3. (Original post by BobbyFlay)
Could you post the actual question please?
It would be a lot easier to understand.
4. (Original post by pineneedles)
I need to use the identity:

sin(A + B) - sin(A - B)/cos(A - B) - cos(A + B) = cotA

along with the exact values of cos 60 and sin 60 to find an exact value for cot 75 in its simplest form. I'm not sure what to do, though.
You need to calculate the value of cot 75.
You need to use the identity cotA = Sin(A+B) etc etc

Put the two together and you realise that A = 75

Therefore cot(75) = sin (75+B)-sin(75-B)/cos(75-B) - cos(75+B)

This is an identity. Which means that for any value of B, the following identity is true.
I could use any value of B I wanted to, such as 64, 10 or 1337.
Can you suggest a value of B that will make things much easier?
Spoiler:
Show
Hint. Look at sin (75+B). What value of B turns it into something you see all the time?
5. (Original post by RMNDK)
You need to calculate the value of cot 75.
You need to use the identity cotA = Sin(A+B) etc etc

Put the two together and you realise that A = 75

Therefore cot(75) = sin (75+B)-sin(75-B)/cos(75-B) - cos(75+B)

This is an identity. Which means that for any value of B, the following identity is true.
I could use any value of B I wanted to, such as 64, 10 or 1337.
Can you suggest a value of B that will make things much easier?
Spoiler:
Show
Hint. Look at sin (75+B). What value of B turns it into something you see all the time?
-15? then you either have 60, or 90, right?
6. (Original post by pineneedles)
-15? then you either have 60, or 90, right?
I wouldn't recommend -15.
That would give cos(90) on the bottom of the fraction which you should just stay away from.
7. (Original post by RMNDK)
I wouldn't recommend -15.
That would give cos(90) on the bottom of the fraction which you should just stay away from.
I'm confused
I used -15 and got 2 - sqrt(3)
What's wrong with having cos90 on the bottom?
8. (Original post by pineneedles)
I'm confused
I used -15 and got 2 - sqrt(3)
What's wrong with having cos90 on the bottom?
Oh sorry!

I thought it was:
sin (75+B)-(sin(75-B)/cos(75-B)) - cos(75+B)

But based on your message I believe the identity is:

(sin (75+B)-sin(75-B))/(cos(75-B) - cos(75+B))

In that case you are perfectly right to use -15.
9. (Original post by RMNDK)
Oh sorry!

I thought it was:
sin (75+B)-(sin(75-B)/cos(75-B)) - cos(75+B)

But based on your message I believe the identity is:

(sin (75+B)-sin(75-B))/(cos(75-B) - cos(75+B))

In that case you are perfectly right to use -15.
That's fine, the problem was the way I'd typed it!

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