Question

Найдите sin A, если : a) ctg A = 2; б) ctg A = 1.​

Answer 1

$a)\; \; ctgA=2\\\\1+ctg^2A=\frac{1}{sin^2A}\; \; \to \; \; sinA=\pm \sqrt{\frac{1}{1+ctg^2A}}=\pm \sqrt{\frac{1}{1+4}}=\pm \sqrt{\frac{1}{5}}=\pm \frac{1}{\sqrt5}=\pm \frac{\sqrt5}{5}\\\\\\2)\; \; ctgA=1\\\\sinA=\pm \sqrt{\frac{1}{1+1}}=\pm \sqrt{\frac{1}{2}}=\pm \frac{1}{\sqrt2}=\pm \frac{\sqrt2}{2}$