SOLUTION: i have to prove this identity: 1/ tanx + tanx = sec^2x/tanx i do have an idea on what to do but i get stuck every time this is what i did 1/ tanx + tanx = sec^2x/tanx cot x

Algebra ->  Trigonometry-basics -> SOLUTION: i have to prove this identity: 1/ tanx + tanx = sec^2x/tanx i do have an idea on what to do but i get stuck every time this is what i did 1/ tanx + tanx = sec^2x/tanx cot x      Log On


   

Question 1057127: i have to prove this identity: 1/ tanx + tanx = sec^2x/tanx
i do have an idea on what to do but i get stuck every time
this is what i did
1/ tanx + tanx = sec^2x/tanx
cot x + 1/ cot x =

Found 2 solutions by solve_for_x, Alan3354:
Answer by solve_for_x(190) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with the left side, combine 1/tan x and tan x into a single fraction.

You can do this by multiplying tax by (tan x / tan x):



Then, from %28sin+x%29%5E2+%2B+%28cos+x%29%5E2+=+1, you can get 1+%2B+%28tan+x%29%5E2+=+%28sec+x%29%5E2%29
by dividing through by %28cos+x%29%5E2

Substituting %28sec+x%29%5E2 in place of 1+%2B+%28tan+x%29%5E2 gives:

1%2Ftan+x+%2B+tan+x+=++%28%28sec+x%29%5E2%29%2F%28tan+x%29%29+

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1/ tanx + tanx = sec^2x/tanx
Multiply by tangent
1 + tan^2 = sec^2
QED