Question

Тригонометрия,срочно,пожалуйста!!!

Answer 1

$tgalpha=frac12; tgbeta=frac13; pi<alpha+beta<2pi;\ alpha+beta-?;\ tg(alpha+beta)=frac{sin(alpha+beta)}{cos(alpha+beta)}=frac{sinalphacosbeta+cosalphasinbeta}{cosalphacosbeta-sinalphasinbeta}=\ =frac{sinalphacosbeta+cosalphasinbeta}{cosalphacosbeta-sinalphasinbeta}cdotfrac{frac{1}{cosalphacosbeta}}{frac{1}{cosalphacosbeta}}=$
$=frac{frac{sinalphacosbeta+cosalphasinbeta}{cosalphacosbeta}}{frac{cosalphacosbeta-sinalphasinbeta}{cosalphacosbeta}}=frac{tgalpha+tgbeta}{1-tgalphacdot tgbeta}=frac{frac12+frac13}{1-frac12cdotfrac13}=\ =frac{frac{3+2}{2cdot3}}{1-frac16}=frac{frac56}{frac56}=1;\ tg(alpha+beta)=1; pi<alpha+beta<2pi;\ alpha+beta=pi+fracpi4=frac{5pi}{4}$



$left { {{sin xsin y=frac14} atop {ctg xcdot ctg y=3}} right.; \ cos(x-y)-?;\ D(f): x,yneq pi k, kin Z;\ ctgxcdot ctgy=frac{cos xcdotcos y}{sin xcdotsin y}=frac{cos xcos y-sin xsin y+sin xsin y}{sin xsin y}=$
$frac{(cos xcos y+sin xsin y)-sin xsin y}{sin xsin y}=frac{cos(x-y)-sin xsin y}{sin xsin y}=ctgxcdot ctgy;\ cos(x-y)=ctgxcdot ctgycdotsin xcdotsin y+sin xsin y=\ =sin xcdotsin ycdot(ctgxcdot ctgy+1)=frac14cdot(3+1)=frac14cdot4=1;\ cos(x-y)=1$

Answer 2

Громадное спасибо!

Answer 3

1)tg(a+b)=(tga+tgb)/(1-tgatgb)=(1/2+1/3):(1-1/2*1/3)=(3/6+2/6):(1-1/6)=5/6:5/6=1
a+b=π/4+πn U π<a+b<2π⇒a+b=5π/4
2)sinxsiny=1/4
ctgx*ctgy=cosxcosy/sinxsiny=3⇒cosxcosy=3*1/4=3/4
cos(x-y)=cosxcosy+sinxsiny=3/4+1/4=1