Question

Найдите значения выражения

Answer 1

$4)\; \; tga=\frac{3}{2}\; ,\; \; \frac{sina\, cosa}{sin^2a-cos^2a}=\frac{cos^2a\cdot tga}{cos^2a\cdot (tg^2a-1)}=\frac{tga}{tg^2a-1}=\frac{3/2}{9/4-1}=\frac{6}{5}\\\\\\5)\; \; sina=\frac{2}{3}\; \; ,\; \; \frac{1-tg^2a}{1-ctg^2a}=\frac{1-\frac{sin^2a}{cos^2a}}{1-\frac{cos^2a}{sin^2a}}=\frac{(cos^2a-sin^2a)\cdot sin^2a}{(sin^2a-cos^2a)\cdot cos^2a}=\\\\\star \; \; cos^2a=1-sin^2a=1-\frac{4}{9}=\frac{5}{9}\; \; \star \\\\=\frac{(\frac{5}{9}-\frac{4}{9})\cdot \frac{4}{9}}{(\frac{4}{9}-\frac{5}{9})\cdot \frac{5}{9}}=-\frac{4}{5}$

$6)\; \; cosa=-\frac{1}{3}\; \; ,\; \; \frac{1-tg^2a}{1-ctg^2a}=\frac{(cos^2a-sin^2a)\cdot sin^2a}{(sin^2a-cos^2a)\cdot cos^2a}=\\\\\star \; \; sin^2a=1-cos^2a=1-\frac{1}{9}=\frac{8}{9}\; \; \star \\\\=\frac{(\frac{1}{9}-\frac{8}{9})\cdot \frac{8}{9}}{(\frac{8}{9}-\frac{1}{9})\cdot \frac{1}{9}}=\frac{-\frac{7}{9}\cdot \frac{8}{9}}{\frac{7}{9}\cdot \frac{1}{9}}=-\frac{8}{1}=-8$