# Trig Identity Problem

• April 18th 2009, 03:22 PM
tleave2000
Trig Identity Problem
I'm having trouble with this trig identity:

$\frac{cosA}{1-tanA}+\frac{sinA}{1-cotA}\equiv sinA + cosA$

It seems I'll have to add the two fractions on the LHS to get the RHS.

$\frac{cosA+sinA-cosAcotA-sinAtanA}{2-cotA-tanA}$

After that I don't know what I can do to simplify it to get the RHS. Any hints/solutions would be welcome. Thanks in advance.
• April 18th 2009, 03:48 PM
stapel
Try converting everything on the left-hand side to sines and cosines.

The first fraction should simplify as (cos^2(A))/(cos(A) - sin(A)).

The second fraction should simplify as (sin^2(A))/(sin(A) - cos(A)).

Note that sin(A) - cos(A) = -[cos(A) - sin(A)], and combine the fractions.

Factor the difference of squares in the numerator. Cancel the common factor.

What are you left with? :wink:
• April 18th 2009, 04:07 PM
tleave2000
Awesome, thanks a lot!