SOLUTION: Hi, I have been agonizing over this one for more than an hour already, so I hope someone can explain this to me... tan30 + tan45 ----------- ---- 1

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Question 601853: Hi, I have been agonizing over this one for more than an hour already, so I hope someone can explain this to me...
tan30 + tan45
----------------
1 - tan30 tan45

= 1/sqrt3 + 1
----------------- ((1))
1 - (1/sqrt3)(1)

= 1 + sqrt3 / sqrt3
-------------------- ((2))
sqrt3 - 1 / sqrt3
= (1 + sqrt3/ sqrt3 - 1) x (sqrt3 + 1/ sqrt3 + 1) ((3))
= (1+ sqrt3)(sqrt3 + 1)
----------------------- ((4))
3-1
= sqrt3 + 1 + 3 + sqrt3
----------------------- ((5))
2
= 4 + 2 sqrt3
-------------- ((6))
2
= 2(2+ sqrt3)
-------------- ((7))
2
= 2+sqrt3 ((8))

My question is, in ((2)), how did 1 become negative? Shouldn't it be 1 - sqrt3 instead of sqrt3 - 1?
I understand that 1/sqrt3 becomes sqrt3/3 after multiplying it by sqrt3/sqrt3 to get rid of the square root in the decimal, but I really don't get what happened with 1.
What am I doing wrong? I just can't get to the final answer no matter what I do. Please help me. Thank you.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Hi, I have been agonizing over this one for more than an hour already, so I hope someone can explain this to me...
tan30 + tan45
----------------
1 - tan30 tan45
= 1/sqrt3 + 1
----------------- ((1))
1 - (1/sqrt3)(1)
= 1 + sqrt3 / sqrt3 ************** Num is 1 + sqrt(3)/3 = (3+sqrt(3))/3
-------------------- ((2))
sqrt3 - 1 / sqrt3
= (1 + sqrt3/ sqrt3 - 1) x (sqrt3 + 1/ sqrt3 + 1) ((3))
= (1+ sqrt3)(sqrt3 + 1)
----------------------- ((4))
3-1
= sqrt3 + 1 + 3 + sqrt3
----------------------- ((5))
2
= 4 + 2 sqrt3
-------------- ((6))
2
= 2(2+ sqrt3)
-------------- ((7))
2
= 2+sqrt3 ((8))

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
(tan30 + tan45)
----------------
(1 - tan30 tan45)
= (1/sqrt3 + 1)
-----------------
(1 - (1/sqrt3)(1))
= [(1 + sqrt3) / sqrt3]
--------------------
[(sqrt(3)-1)]/sqrt(3)]
====================================
Invert the denominator and multiply:
---
= [(1 + sqrt3) / sqrt3]
----------------------------------------
-----
Cancel the common sqrt(3) to get:
= [1+sqrt(3)]/[(1-sqrt(3))]
-----
Multiply numerator and denominator by (1+sqrt(3) to get
----
= [1+sqrt(3)]^2 / [1-3]
---
= [1 + 2sqrt(3) + 3]/(-2)
---
= [4 + 2sqrt(3)]/(-2)
----
= -2 -sqrt(3)
=======================
Cheers,
Stan H.

SOLUTION: Hi, I have been agonizing over this one for more than an hour already, so I hope someone can explain this to me... tan30 + tan45 ----------- ---- 1 - tan30 tan45 = 1/sqr