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Please help me prove this trig identity?

I have to prove that:

(tan(A+B) - tanA) / (1+tan(A+B)tanA) is equal to tanB

I've tried subbing in tan(A+B) is equal to (tanA+tanB) / (1-tanAtanB) but I just end up with huge fractions that don't seem like there gonna cancel down.

Can someone please help me?

Thanks :smile:
Original post by tinto99
I have to prove that:

(tan(A+B) - tanA) / (1+tan(A+B)tanA) is equal to tanB

I've tried subbing in tan(A+B) is equal to (tanA+tanB) / (1-tanAtanB) but I just end up with huge fractions that don't seem like there gonna cancel down.

Can someone please help me?

Thanks :smile:


It is much, much easier than what you have tried.

think how you can directly re-write (tan(A+B) - tanA) / (1+tan(A+B)tanA) using an identity not too dis-similar from the tan(A+B) that you tried !!!!

the answer falls out in perhaps 2 lines at most !!
Reply 2
Avatar for tinto99
tinto99
OP
1
Original post by H.C. Chinaski
It is much, much easier than what you have tried.

think how you can directly re-write (tan(A+B) - tanA) / (1+tan(A+B)tanA) using an identity not too dis-similar from the tan(A+B) that you tried !!!!

the answer falls out in perhaps 2 lines at most !!


I don't know of any other tan identities, aside from sin/cos. Is that what you meant?
Reply 3
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nuodai
17
Original post by tinto99
I don't know of any other tan identities, aside from sin/cos. Is that what you meant?


It's not what he meant. It might help you to write C=A+BC=A+B, then then try and write BB in terms of AA and CC. Having written BB in terms of AA and CC, expand tan⁡B\tan B and compare with what you have.
Reply 4
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tinto99
OP
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Original post by nuodai
It's not what he meant. It might help you to write C=A+BC=A+B, then then try and write BB in terms of AA and CC. Having written BB in terms of AA and CC, expand tan⁡B\tan B and compare with what you have.


i'm trying that at the moment with no luck :frown:

so if tan(A+B)=tanC, do I rewrite the whole thing as:

(tanC-tanA) / (1+tanCtanA)

even so, i still wouldn't know what to do from there. this is my homework after my second lesson of C3 trig, i managed to do all the others, this is the last one and i just can't do it :mad:
Reply 5
Avatar for GANDULF
GANDULF
i tried subing the identity and it worked
open the attachment to see the working.
(edited 12 years ago)
Photo on 2011-09-26 at 18.38.jpg46.8KB
Reply 6
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TenOfThem
18
You want to use

B = (A + B) - A
Reply 7
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tinto99
OP
1
Original post by GANDULF
i tried subing the identity and it worked
open the attachment to see the working.


thank you, im also gonna try using the A B and C terms to see if I can do it that way as well :smile:
Original post by tinto99
thank you, im also gonna try using the A B and C terms to see if I can do it that way as well :smile:


Write down the identity for Tan (x-y)

Now let x = A+B and let y=A substitute this in to the identity for Tan(x-y)

Now have a look at the thing and see why it helps with your problem .....

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