Question 923335
Prove that:
TanA - CotA = -2Cot2A
***
use x for A
{{{tanx-cotx=-2cot^2(x)}}}
start with left side:
{{{tanx-cotx=sinx/cosx-cosx/sinx
=(sin^2(x)-cos^2(x))/sinxcosx
=-((cos^2(x)-sin^2(x)))/sinxcosx=-cos(2x)/sinxcosx
=-2*cos(2x)/(2*sinxcosx)=-2cos(2x)/(sin(2x))=-cot(2x)}}}
verified: left side=right side