1-sin^4 а- cos^4 а/ cos^4a

(1- sin^4a-cos^4a)/cos^4a   = (4-3-cos4a/4) /cos^4a = (1-cos4a)/4cos^4a =  (8cos^2a- 8 cos^4a)/4cos^4a =  (2/cos^2a) -2=(2-2cos^2a)/cos^2a    

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