Question

ctg ⁡α/2-tgα/2=2ctg ⁡α

Answer 1

$ctgfrac{ alpha }{2}-tgfrac{ alpha }{2}=frac{cosfrac{ alpha }{2}}{sinfrac{ alpha }{2}}-frac{sinfrac{ alpha }{2}}{cosfrac{ alpha }{2}}=frac{cos^2frac{ alpha }{2}-sin^2frac{ alpha }{2}}{sinfrac{ alpha }{2}cosfrac{ alpha }{2}}=\=frac{cos alpha }{frac{1}{2}sin alpha }=2frac{cos alpha }{sin alpha }=2ctg alpha$