SOLUTION: PLEASE PLEASE HELP!!!!!!!!!!!!!!!!! show that they equal. 1 + cot 30 degrees cot 60 degrees/cot 30 degrees-cot 60 degrees=cot 30 degrees.

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Question 181074: PLEASE PLEASE HELP!!!!!!!!!!!!!!!!!
show that they equal.
1 + cot 30 degrees cot 60 degrees/cot 30 degrees-cot 60 degrees=cot 30 degrees.
Found 2 solutions by eperette, solver91311:
Answer by eperette(173) (Show Source):
You can put this solution on YOUR website!
THINGS YOU SHOULD KNOW:
cot 30 = cos 30/sin30 = (sqr(3)/2)/(1/2)= sqr(3)
cot 60 = cos60/sin60 = (1/2)/ (sqr (3)/2)= 1/ sqr(3) = sqr(3)/3
(1 + cot30 cot60)/ (cot30-cot60)
(1 + sqr(3)*sqr(3)/3)/ (sqr(3)- sqr(3)/3)
(1 + 3/3)/ (3sqr(3)/3 - sqr(3)/3)
(1 + 1)/ (2sqr(3)/3)
2/ (2sqr(3)/3)
(2/1)(3/ 2sqr(3))
3/sqr(3)
3/sqr(3) * (sqr(3)/sqr(3))
3sqr(3)/3
sqr(3)
and sqr(3)= cot30

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Use the identity

And the facts that:
30 degrees =

60 degrees =

Hence:

and

John