tanx+cotx=sinx/cosx+cosx/sinx=(sin^2x+cos^2x)/sinxcosx=1/sinxcosxsinx+cosx=√2(√2/2sinx+√2/2cosx)=√2sin(x+π/4 )sin(π/4 + 2/x)=sin[π/2-(π/4 - x/2)]=cos(π/4 - x/2)