Вычислите: 1) 2) 3)

Решите задачу:

$1) arcsin\frac{ \sqrt{5} }{3}=a\\ sina = \frac{ \sqrt{5} }{3} \\ cosa=2cos^2\frac{1}{2} a-1= \sqrt{1-sin^2a} = \sqrt{1- \frac{5}{9} } = \frac{2}{9} \\ cos^2\frac{1}{2} a= \frac{11}{18} \\ cos\frac{1}{2} a= \frac{ \sqrt{22} }{6}$

$2)arcctg(ctg10)=10$

$3)sin(5arccosx) \\ arccosx=a\\ cosa=x\\ sin(5a)=16sin^5(a)-20sin^3(a)+5sin(a) =\\=sina(sin^2a(16sin^2a-20)+5)=\\ = \sqrt{1-x^2} ((1-x^2)(16-16x^2-20)+5)=\\ = \sqrt{1-x^2} ((x^2-1)(16x^2-4)+5)=\\ = \sqrt{1-x^2} (16x^4-20x^2+9)$