[tex]\displaystyle 1)sin(\alpha )^2-sn(\alpha)^2cos(\alpha )^2=(1-cos(\alpha ^2)*sin(\alpha )^2=sin(\alpha )^2sin(\alpha )^2=sin(\alpha )^4\\\\2)sin(\alpha )^2+cos(\alpha )^2+tg(\alpha )^2=1+tg(\alpha )^2=sec(\alpha )^2\\\\3)\frac{tg(\alpha )}{ctg(\alpha )}+1=\frac{tg(\alpha )}{\frac{1}{tg(\alpha )} }+1=tg(\alpha )^2+1=sec(\alpha )^2[/tex]