Помогите с алгеброй. спасибо заранее.

1) $\displaystyle tg^2a-sin^2a-tg^2a*sin^2a=tg^2a(1-sin^2a)-sin^2a=$

$\displaystyle= \frac{sin^2a}{cos^2a}*cos^2a-sin^2a=sin^2a-sin^2a=0$

2) $\displaystyle \sqrt{sin^2b(1+ctgb)+cos^2b(1+ctgb)}=$

$\displaystyle \sqrt{sin^2b+ \frac{sin^2b*cosb}{sinb}+cos^2b+ \frac{cos^2b*sinb}{cosb}}=$

$\displaystyle= \sqrt{sin^2b+sinbcosb+cos^2b+cosbsinb}= \sqrt{(cosb+sinb)^2}=$

$\displaystyle=|cosb+sinb|$

3) $\displaystyle (3sina+2cosa)^2+(2sina-3cosa)^2=9sin^2a+12sinacosa+4cos^2a+$
$\displaystyle+4sin^2a-12sinacosa+9cos^2a=12sin^2a+12cos^2a=12$

4) $\displaystyle \frac{cosb*tgb}{sin^2b}-ctgb*cosb= \frac{cosb* \frac{sinb}{cosb}}{sin^2b}- \frac{cosb}{sinb}*cosb= \frac{1}{sinb}- \frac{cos^2b}{sinb}=$

$\displaystyle= \frac{1-cos^2b}{sinb}= \frac{sin^2b}{sinb}=sinb$