Question

A+B+C=180, then Σ tan(A/2)tan(B/2)= ?

Answer 1

i'll post what all I know :

Answer 2

A+B=180-C
And.. We need to find - tan a/2 tan b/2 + tan b/2 tan c/2+ tan c/2 tan a/2

Answer 3

@hartnn

Answer 4

@phi

Answer 5

@campbell_st

Answer 6

@thomaster

Answer 7

@AccessDenied

Answer 8

@Preetha

Answer 9

@tHe_FiZiCx99

Answer 10

@nincompoop

Answer 11

@Destinymasha

Answer 12

@campbell_st

Answer 13

@poopsiedoodle

Answer 14

just a second let me do something for spanish class really quick and I'll take a look at it

Answer 15

Thank you :) take your time :)

Answer 16

Hmm... So, it A+2B = 180, and A+B = 180 - C, then B must equal C.

Answer 17

And if that's the case, then A+2C = 180, and A+C = 180 - C.

Answer 18

Oh i'm extremely sorry, it ain't a+b+b, it's a+b+c. .. M mistake

Answer 19

oh lol. Just a second then

Answer 20

lol

Answer 21

A + B = 180 - C. So, I guess we're going to try to make some substitution happen here. A = 180 - C - B.

Answer 22

So, 180 - C - B + B = 180 - C.

Answer 23

Aaaaaaaaaaaaand that gets us nowhere, because after simplifying, we get 180 - C = 180 - C. Great.

Answer 24

Haha..

Answer 25

What if we convert tan in terms of sin's and cos' ?

Answer 26

In that case, it looks like I don't quite know what I'm doing here. Soooooo, @mathmale. And I dunno. Let's try that, I guess. This is a triangle we're working with here, right?

Answer 27

i tried doing it that way, but it doesn't really took me anywhere.. :(

Answer 28

Yep. Right.

Answer 29

Any side lengths given?

Answer 30

didn't *

Answer 31

Nopes. Just what i wrote in the question.

Answer 32

Well dag, yo.

Answer 33

Well, I dunno, it looks like 2 might be a side length, because tan(A/2) and such. When you do tangents, you divide the opposite side by the adjacent side. So, one of the sides is probs 2.

Answer 34

No no .. i'm afraid that isn't the way we do it :/
Thanks for trying though! :D Thank you!

Answer 35

Lel. Yeah, I'm not too good with geometry. But I tried :p And looks like we have hartnn here now :D

Answer 36

if A+B+C = pi
what does A/2 + B/2 equal ?

Answer 37

i am intending to use
\(\tan (x+y)\)
formula

Answer 38

told ya already - pi/2- c/2

Answer 39

I tried it that way too.. but then it just looked so complicated!

Answer 40

you mean pi/2 - c/2 ?
\(\tan (\pi/2 -C/2) = (1/\tan C/2)\)

now expand \(\large \tan (A/2+B/2)\)
using the formula, what u get ?

Answer 41

did u get how its 1/tan (C/2)
?

Answer 42

tan[a/2]+tan[b/2]/ 1-tan a/2 tan b/2 = cot c/2 = 1/tanc/2

Answer 43

@hartnn

Answer 44

multiply tan c/2 on both sides :)

Answer 45

now its just some re-arrangement of terms

Answer 46

@hartnn - Oh my goodness.. Man, thank you. Thank you so very much!
Thanks a ton! :)))

Answer 47

you're most welcome ^_^

Answer 48

Seriously, THANKS A TON!