I'm stuck on a problem, and I want to figure it out so that I will know it later if it might appear on a test or something.

cot2A = 1/2(cotA-tanA)

Thanks!

cot(2A)=\frac{1}{2}(cot(A)-tan(A))

Note the identities: cot(2A)=\frac{cos(2A)}{sin(2A)}

cos(2A)=cos^{2}(A)-sin^{2}(A)

sin(2A)=2sin(A)cos(A)

\frac{cos^{2}(A)-sin^{2}(A)}{2sin(A)cos(A)}

\frac{1}{2}\frac{cos(A)}{sin(A)}-\frac{1}{2}\frac{sin(A)}{cos(A)}

=\frac{1}{2}cot(A)-\frac{1}{2}tan(A)

\frac{1}{2}(cot(A)-tan(A))