Question

1)Упростите выражение:
cos²α - sin2α / 2ctg α;
2)Вычислите 1 + cos2α при sin²α = 0,74

Answer 1

$1)Cos^{2}\alpha-\frac{Sin2\alpha}{2Ctg\alpha}=Cos^{2}\alpha-\frac{2Sin\alpha Cos\alpha}{\frac{2Cos\alpha}{Sin\alpha}}=Cos^{2}\alpha-\frac{2Sin\alpha Cos\alpha*Sin\alpha}{2Cos\alpha}=Cos^{2}\alpha-Sin^{2}\alpha=Cos2\alpha\\\\Otvet:\boxed{Cos2\alpha}$

$2)1+Cos2\alpha=1+1-2Sin^{2}\alpha=2-2Sin^{2}\alpha=2-2*0,74=2-1,48=0,52\\\\Otvet:\boxed{0,52}$