Question

Сростіть вираз
1-2ctg5a/sin 10a

Answer 1

$1-\frac{2ctg(5a)}{sin(10a)}=1-2ctg(5a)\cdot \frac{1}{sin(2\cdot 5a)}=1-\frac{2cos(5a)}{sin(5a)}\cdot \frac{1}{2sin(5a)cos(5a)}=1-\frac{1}{sin^2(5a)}=\frac{sin^2(5a)-1}{sin^2(5a)}=\frac{-cos^2(5a)}{sin^2(5a)}=-ctg^2(5a)$