Question

Помогите решить логарифм и тождество...

Answer 1

$log_2(3-x)+log_2(1-x)=3\O.D.3.:\begin{cases}3-x textgreater 0\1-x textgreater 0end{cases}Rightarrowbegin{cases}x textless 3\x textless 1end{cases}Rightarrow x textless 1\log_2(3-x)(1-x)=3\(3-x)(1-x) = 2^3\3-4x+x^2=8\x^2-4x-5=0\D=16+4cdot5=36\x_{1,2}=frac{4pm6}2\x_1=-1\x_2=5;-;He;nogx.;no;O.D.3.$

$tgalpha+tgbeta=frac{sinalpha}{cosalpha}+frac{sinbeta}{cosbeta}=frac{sinalphacosbeta+sinbetacosalpha}{cosalphacosbeta}=\=frac{frac{sin(alpha-beta)+sin(alpha+beta)}2+frac{sin(beta-alpha)+sin(beta+alpha)}2}{cosalphacosbeta}=\=frac{sin(alpha-beta)+sin(alpha+beta)-sin(alpha-beta)+sin(alpha+beta)}{2cosalphacosbeta}=frac{2sin(alpha+beta)}{2cosalphacosbeta}=frac{sin(alpha+beta)}{2cosalphacosbeta}$