Rút gọn biểu thức \( T = (1 + cos\alpha )(1 - cos\alpha ) - ta{n^2}\alpha + si{n^2}\alpha .ta{n^2}\alpha \)

* Hướng dẫn giải

Ta có:

\(\begin{array}{l} T = (1 - co{s^2}\alpha ) - ta{n^2}\alpha (1 - si{n^2}\alpha ) = si{n^2}\alpha - ta{n^2}.co{s^2}\alpha \\ = si{n^2}\alpha - \frac{{si{n^2}\alpha }}{{co{s^2}\alpha }}.co{s^2}\alpha = si{n^2}\alpha - si{n^2}\alpha = 0 \end{array}\)