Question

Надо упростить выражение,молю

Answer 1

$1); ; (tgbeta +ctgbeta )^2-(tgbeta -ctgbeta )^2=[, A^2-B^2=(A-B)(A+B), ]=\\=(tgbeta +ctgbeta -(tgbeta -ctgbeta ))cdot (tgbeta +ctgbeta +(tgbeta -ctgbeta ))=\\=2ctgbeta cdot 2tgbeta =4cdot (underbrace {tgbeta cdot ctgbeta }_{1})=4cdot 1=4$

$2); ; tgx+frac{cosx}{1+sinx} =frac{sinx}{cosx}+frac{cosx}{1+sinx}=frac{sinx(1+sinx)+cos^2x}{cosx(1+sinx)}=\\=frac{sinx+sin^2x+cos^2x}{cosx(1+sinx)}=frac{sinx+1}{cosx(1+sinx)} =frac{1}{cosx}\\3); ; frac{1-sina}{cosa}-frac{cosa}{1+sina}=frac{(1-sina)(1+sina)-cos^2a}{cosa(1+sina)}=frac{1-sin^2a-cos^2a}{cosa(1+sina)}=\\=frac{1-(sin^2a+cos^2a)}{cosa(1+sina)}=frac{1-1}{cosa(1+sina)}=0$