Question

tgα+ctgα=√8 0<α<$frac{pi }{4}$
Найти: tgα-ctgα

Answer 1

$0<a<frac{pi }{4}; ; to ; ; 0<tga<1; ,; ; 0<ctga<1; ; i; ; underline {ctga>tga}\\tga+ctga=sqrt8\\(tga+ctga)^2=8\\tg^2a+2, underbrace {tgacdot ctga}_{1}+ctg^2a=8\\tg^2a+2+ctg^2a=8\\tg^2a+ctg^2a=6\\\(tga-ctga)^2=tg^2a+ctg^2a-2=6-2=4; ; to \\(tga-ctga)=2; ; ; ili; ; ; (tga-ctga)=-2\\ctga>tga; ; Rightarrow ; ; underline {tga-ctga=-2}$