Tg²b-sin²b×tg²b помогите упростить к завтра надо

[latex]tg^2b-sin^2b*tg^2b=\\ tg^2b-sin^2b*\frac{sin^2b}{cos^2b}=\\ \frac{sin^2b}{cos^2b}-\frac{sin^4b}{cos^2b}=\\ \frac{sin^2b-sin^4b}{cos^2b}=\\ \frac{1-cos^2b-(1-cos^2b)^2}{cos^2b}=\\ \frac{1-cos^2b-1+2cos^2b-cos^4b}{cos^2b}=\frac{cos^2b-cos^4b}{cos^2b}=\\ 1-cos^2b=sin^2b[/latex]