Question

(1+tg^2(-a))*(1/(1+ctg^2(-a)))

Answer 1

$(1+tg^2(-a))\cdot \frac{1}{1+ctg^2(-a)}=\frac{1}{cos^2(-a)}\cdot \frac{1}{\frac{1}{sin^2(-a)}}=\frac{sin^2a}{cos^2a}=tg^2a\\\\\\\star \; \; 1+tg^2x=\frac{1}{cos^2x}\; \; \star \\\\\star 1+ctg^2x=\frac{1}{sin^2x}\; \; \star \\\\\star \; \; tg(-x)=-tgx\; \; ,\; \; ctg(-x)=-ctgx\; \; \star$