Question

Тригонометрия Плиззззззззз 39 б

Answer 1

$4. cos47*cos17+sin47*sin17=cos(47-17)=cos30=0.5$

$5. frac{sin(alpha-beta)+2cosalpha*sinbeta}{2cosalpha *cosbeta* cos(alpha-beta)}=frac{sinalpha*cosbeta-cosalpha*sinbeta+2cosalpha*sinbeta}{(cos(alpha+beta)+cos(alpha-beta))*cos(alpha-beta)}=\=frac{sinalpha*cosbeta+cosalpha*sinbeta}{(cos(alpha+beta)+cos(alpha-beta))*cos(alpha-beta)}=frac{sin(alpha+beta)}{cos(alpha+beta)cos(alpha-beta)+cos^2(alpha-beta)}=\=frac{2sin(alpha+beta)}{cos2alpha*cos2beta+cos^2(alpha-beta)}=$
$frac{2sin(alpha+beta)}{1/2(cos2(alpha+beta)+cos2(alpha-beta))+cos^2(alpha-beta)}=\=frac{2sin(alpha+beta)}{1/2(2cos^2(alpha+beta)-1+2cos^2(alpha-beta)-1)+cos^2(alpha-beta)}=\=frac{2sin(alpha+beta)}{cos^2(alpha+beta)+cos^2(alpha-beta)-1+cos^2(alpha-beta)}=\=frac{2sin(alpha+beta)}{2cos^2(alpha-beta)-sin^2(alpha+beta)}$

$6. frac{sin(2pi-alpha)*tg(pi/2+alpha)-ctg(3pi/2-alpha)}{cos(2pi+alpha)*tg(pi-alpha)}=frac{-sinalpha*(-ctgalpha)-tgalpha}{cosalpha*(-tgalpha)}=\=frac{sinalpha*frac{cosalpha}{sinalpha}-frac{sinalpha}{cosalpha}}{-cosalpha*frac{sinalpha}{cosalpha}}=frac{cos^2alpha-sinalpha}{-cosalpha*sinalpha}=-frac{cosalpha}{sinalpha}+frac{1}{cosalpha}=secalpha-ctgalpha$

Answer 2

скидываю еще одно