Question

.............Решите...​

Answer 1

$\displaystyle\bf\\8) \ 2Cos^{2} \alpha -\Big(\frac{1}{Sin^{2} \alpha } -Ctg^{2} \alpha \Big)=2Cos^{2} \alpha -\Big(1+Ctg^{2} \alpha -Ctg^{2} \alpha \Big)=\\\\2Cos^{2}\alpha -1 =2Cos^{2} \alpha-(Sin^{2} \alpha +Cos^{2} \alpha)=2Cos^{2}\alpha -Sin^{2} \alpha -Cos^{2} \alpha =\\\\\\=Cos^{2} \alpha -Sin^{2} \alpha =Cos2\alpha \\\\\\9) \ 5-6Cos^{2} \alpha =5-6\cdot(1-Sin^{2} \alpha )=5-6+6Sin^{2}\alpha =\\\\=6Sin^{2} \alpha -1=6\cdot\Big(-\frac{3}{8} \Big)^{2} -1=6\cdot\frac{9}{64} -1=$

$\displaystyle\bf\\=\frac{54}{64} -1=0,84375-1=-0,15625$