Упростите выражение 3sin^2a+cos^4a/1+sin^2a+sin^4a

[latex] \frac{3sin^2a+cos^4a}{1+sin^2a+sin^4a} =\frac{2sin^2a+sin^2a+cos^2a*cos^2a}{1+sin^2a+sin^2a*sin^2a}= \\ =\frac{2sin^2a+sin^2a+cos^2a(1-sin^2a)}{1+sin^2a+sin^2a(1-cos^2a)}=\frac{2sin^2a+sin^2a+cos^2a-sin^2a*cos^2a}{1+sin^2a+sin^2a-sin^2a*cos^2a}=[/latex] [latex]\frac{2sin^2a+1-sin^2a*cos^2a}{1+2sin^2a-sin^2a*cos^2a}=1[/latex]