Question

Выражение: а)cos^2t*tg^2t-sin^2t*cos^2t б)1-сos^2+tg^2t*cos^2t в)(1-sin^2t)*(tg^2t+1) г)(1-cos^2t)*(ctg^2t+1)

Answer 1

А)
$cos^{2} t*tg^{2} t-sin^{2}t*cos^{2} t= \frac{cos^{2}t*sin^{2}t}{cos^{2}t }-sin^{2}t*cos^{2}t=$
$sin^{2} t-sin^{2}t*cos^{2}t=sin^{2}t*(1-cos^{2}t)=sin^{2}t*sin^{2}t=sin^{4}t$
б)
$1-cos^{2}t+tg^{2}t * cos^{2}t=sin^{2} t+ \frac{sin^{2} t*cos^{2}t }{cos^{2}t }=sin ^{2} t+sin^{2} t=2sin^{2} t$
в)
$(1-sin^{2}t)*(tg^{2}t+1)=cos^{2}t*( \frac{sin^{2t} }{cos^{2}t } +1)=sin^{2}t+cos^{2}t=1$
г)
$(1-cos^{2} t)*(ctg^{2}t+1)=sin^{2}t*( \frac{cos^{2}t }{sin^{2}t } +1)=cos^{2}t+sin^{2}t=1$