trig identity problem

[dlthompson81]

I've got this trig problem, I've been struggling with this one for a while. I've tried a couple dozen different ways and still haven't been able to prove it. Any help would be appreciated.

(cot?/1-tan?) + (tan?/1-cot?) = 1 + tan? + cot?

or to make it more easily readable i guess

cot? tan?
-------- + --------- = 1 + tan? + cot?
1-tan? 1-cot?

 

[swaroop]

Convert all possible to terms to a single term, (note i am using x in place of theta)
since cot(x)=1/tan(x)
1/(tanx*(1-tanx)) + tan^2(x)/(tanx-1)
=(1-tan^3(x))
----------------- (The negative sign in the num because we write tanx-1 in the denom as -(1-tanx)
tanx*(1-tanx)
Since a^3-b^3=(a-b)(a^2+ab+b^2)

The expression becomes:
(1-tanx)(1+tanx+tan^2(x))
-------------------------------
tanx(1-tanx)

==> (1+tanx+tan^2(x))
----------------------
tanx
=> cotx+1+tanx which is the RHS terms