1-sin^4t-cos^4t/2sin^4t

Числитель =

=1 - Sin^4 t - Cos^4 t = (1 - Sin²t) (1+Sin²t) - Cos^4t=

=Cos²t (1 + Sin²t) - Cos^4 t = Cos²t + Sin²tCos²t - Cos^4 t=

= Cos²t (1 - Cos²t) + Sin²tCos²t = Cos²t·Sin²t+Sin²tCos²t=

=2Sin²tCos²t

При делении на 2Sin^4 t дробь можно сократить на 2 Sin²t

Ответ: Сtg² t