Chứng minh sin^22x- 4sin ^2x/sin ^22x + 4sin ^2x - 4 = tan ^4x

Lời giải

Ta có \(\frac{{{{\sin }^2}2{\rm{x}} - 4{{\sin }^2}x}}{{{{\sin }^2}2{\rm{x + }}4{{\sin }^2}x - 4}}\)

= \(\frac{{ - 4{{\sin }^4}x}}{{ - 4c{\rm{o}}{{\rm{s}}^4}x}} = {\tan ^4}x\)

Vậy \(\frac{{{{\sin }^2}2{\rm{x}} - 4{{\sin }^2}x}}{{{{\sin }^2}2{\rm{x + }}4{{\sin }^2}x - 4}} = {\tan ^4}x\).