Question

Помогите пожалуйста
1) ctg(arcsin1/5)
2) sin²(1/2arcsin1/4)-cos²(1/2arcsin1/4)
3) cos(arccos3/4-arcsin1/3)

Answer 1

$1) ctg(arcsin1/5)=frac{cos(arcsin1/5)}{sin(arcsin1/5)}=frac{sqrt{1-sin^2(arcsin1/5)}}{1/5}=frac{sqrt{1-(1/5)^2}}{1/5}=\= frac{sqrt{24}}{5}:frac{1}{5}=sqrt{24}$

$2) sin^2(1/2arcsin1/4)-cos^2(1/2arcsin1/4)=[arcsin1/4=alpha]=\= sin^2frac{alpha}{2}-cos^2frac{alpha}{2}=-cosalpha=-cos(arcsin1/4)=\=-sqrt{1-sin^2(arcsin1/4)}=-sqrt{1-1/16}=-frac{sqrt{15}}{4}$

$3) cos(arccos3/4-arcsin1/3)=[arccos3/4=alpha, arcsin1/3=beta]=\=cos(alpha-beta)=cosalpha*cosbeta+sinalpha*sinbeta=\= cos(arccos3/4)*cos(arcsin1/3)+sin(arccos3/4)*sin(arcsin1/3)=\= 3/4*sqrt{1-1/9}+sqrt{1-9/16}*1/3=frac{3}{4}*frac{sqrt8}{3}+frac{sqrt7}{4}*frac{1}{3}=\=frac{sqrt2}{2}+frac{sqrt7}{12}=frac{6sqrt2+sqrt7}{12}$

Answer 2

Спасибо,очень благодарна