Question

Скоротити: $(1+ctg \beta )^{2} + (1- ctg \beta )^{2}$

Answer 1

$\displaystyle\bf\\(1+Ctg\beta )^{2} +(1-Ctg\beta )^{2} =\\\\\\=1+2Ctg\beta +Ctg^{2} \beta +1-2Ctg\beta +Ctg^{2} \beta =2+2Ctg^{2} \beta =\\\\\\=2\cdot(1+Ctg^{2} \beta )=2\cdot\frac{1}{Sin^{2} \beta } =\frac{2}{Sin^{2} \beta }$