Question

4. Упростите выражение: (sin²a - tg²a) . cos²a​

Answer 1

$\displaystyle\bf\\\Big(Sin^{2} \alpha -tg^{2} \alpha \Big)\cdot Cos^{2} \alpha =\Big(Sin^{2} \alpha -\frac{Sin^{2} \alpha }{Cos^{2} \alpha } \Big)\cdot Cos^{2} \alpha =\\\\\\=\frac{Sin^{2} \alpha \cdot Cos^{2} \alpha -Sin^{2}\alpha }{Cos^{2} \alpha } \cdot Cos^{2} \alpha= Sin^{2} \alpha \cdot Cos^{2} \alpha -Sin^{2}\alpha=\\\\\\=Sin^{2} \alpha \cdot \Big(Cos^{2} \alpha -1\Big)=Sin^{2} \alpha \cdot(-Sin^{2} \alpha )=-Sin^{4} \alpha$