Chứng minh đẳng thức tan^2x - sin^2x = tan^2x . sin^2x

Đề bài: Chứng minh đẳng thức: tan^2x - sin^2x = tan^2x . sin^2x

Trả lời

Hướng dẫn giải:

$$\begin{gathered} {\text{tan}}^{\text{2}}{\text{x - sin}}^{\text{2}}\text{x = }\frac{{\text{sin}}^{\text{2}}\text{x}}{{\text{cos}}^{\text{2}}\text{x}}{\text{ - sin}}^{\text{2}}{\text{x = sin}}^{\text{2}}\text{x . }\left(\frac{\text{1}}{{\text{cos}}^{\text{2}}\text{x}}\text{ - 1}\right) \\ {\text{= sin}}^{\text{2}}\text{x . }\frac{{\text{sin}}^{\text{2}}\text{x}}{{\text{cos}}^{\text{2}}\text{x}}{\text{ = tan}}^{\text{2}}{\text{x . sin}}^{\text{2}}\text{x} \end{gathered}$$