A) (cos^2 t - ctg^2 t ) / (sin^2 t - tg^2 t) =?б) (tg t +1) / (1+ctg t) =?ПОМОГИТЕ...

А) $\frac{cos^{2}t-ctg^{2}t}{sin^{2}t-tg^{2}t}$

упростим числитель: $cos^{2}t-\frac{cos^{2}t}{sin^{2}t}=\frac{cos^{2}t*sin^{2}t-cos^{2}t}{sin^{2}t}=\frac{cos^{2}t*(sin^{2}t-1)}{sin^{2}t}=-\frac{cos^{2}t*(1-sin^{2}t)}{sin^{2}t}=$ $-\frac{cos^{4}t}{sin^{2}t}$

упростим знаменатель: $sin^{2}t-tg^{2}t=sin^{2}t-\frac{sin^{2}t}{cos^{2}t}=\frac{sin^{2}t*cos^{2}t-sin^{2}t}{cos^{2}t}=$ $\frac{sin^{2}t*(cos^{2}t-1)}{cos^{2}t}=-\frac{sin^{2}t*(1-cos^{2}t)}{cos^{2}t}=-\frac{sin^{4}t}{cos^{2}t}$

дробь: $\frac{-\frac{cos^{4}t}{sin^{2}t}}{-\frac{sin^{4}t}{cos^{2}t}}= \frac{cos^{4}t*cos^{2}t}{sin^{4}t*sin^{2}t}=$ $\frac{cos^{6}t}{sin^{6}t}=ctg^{6}t$

Б) $\frac{tgt+1}{1+ctgt}= \frac{tgt+1}{1+ \frac{1}{tgt}}=\frac{tgt+1}{\frac{tgt+1}{tgt}}=\frac{(tgt+1)*tgt}{tgt+1}=tgt$