Question

упростите: Cos^альфа+Ctg^альфа - 1/sin^альфа

Answer 1

$cos^{2}a+ctg^{2}a-frac{1}{sin^{2}a}=frac{cos^{2}a*sin^{2}a}{sin^{2}a}+frac{cos^{2}a}{sin^{2}a}-frac{1}{sin^{2}a}=$

$=frac{cos^{2}a*sin^{2}a+(cos^{2}a-1)}{sin^{2}a}=frac{cos^{2}a*sin^{2}a+sin^{2}a}{sin^{2}a}=frac{sin^{2}a(cos^{2}a+1)}{sin^{2}a}=$

$=cos^{2}a+1$