
Trig Identity Problem
I'm having trouble with this trig identity:
$\displaystyle \frac{cosA}{1tanA}+\frac{sinA}{1cotA}\equiv sinA + cosA$
It seems I'll have to add the two fractions on the LHS to get the RHS.
Adding the fractions gave me:
$\displaystyle \frac{cosA+sinAcosAcotAsinAtanA}{2cotAtanA}$
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.

Try converting everything on the lefthand 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:
