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