[latex]mathrm{(a) sin alpha cdot frac{ctg alpha }{cos alpha }=1 } \ \ mathrm{ L=sin alpha cdot frac{ctg alpha }{cos alpha }=sin alpha cdot frac{cos alpha }{sin alpha } cdot frac{1}{cos alpha }=1=P } [/latex] [latex] mathrm{(b) sin alpha + sin alpha cdot tg^2alpha= frac{tg alpha}{cos alpha} } }[/latex] [latex] mathrm{ L=s in alpha + sin alpha cdot tg^2alpha= sin alpha +sin alpha cdot frac{sin^2 alpha }{cos^2 alpha } =} \ mathrm{ = sin alpha + frac{sin^3 alpha }{cos^2 alpha }= frac{sin alpha cos^2 alpha +sin^3 alpha }{cos^2 alpha }= frac{sin alpha (cos^2 alpha +sin^2 alpha )}{cos^2 alpha }= }}[/latex] [latex]mathrm{= frac{sin alpha (cos^2+1-cos^2 alpha )}{cos^ 2 alpha } = frac{sin alpha }{cos^ alpha }= frac{sin alpha }{cos alpha } cdot frac{1}{cos alpha } =tg alpha cdot frac{1}{cos alpha }=frac{tg alpha }{cos alpha } =P}[/latex]
