Răspuns:
[tex]\frac{sin^{2}2x-4sin^{2}x}{sin^{2}2x+4sin^{2}x-4}= \frac{4sin^{2}xcos^{2}x -4sin^{2}x}{4sin^{2}xcos^{2}x+4sin^{2}x-4}= \frac{4sin^{2}x(cos^{2}x-1)}{4sin^{2}xcos^{2}x+4sin^{2}x-4sin^{2}x-4cos^{2}x}=\\\frac{4sin^{2}x(cos^{2}x-1)}{4sin^{2}xcos^{2}x-4cos^{2}x}=\frac{4sin^{2}x(cos^{2}x-1)}{4cos^{2}x(sin^{2}x-1)}=\frac{sin^{2}x(-sin^{2}x)}{cos^{2}x(-cos^{2}x)}=\frac{sin^{4}x}{cos^{4}x}=tg^{4}x[/tex]
Explicație pas cu pas:
folosesti formulele:
[tex]sin 2x=2sin x cos x[/tex]
[tex]sin^{2}x+cos^{2}x=1[/tex]
