Question

Помогите пожалуйста решить 2 и 3п пример

Answer 1

1)

$tg(-60)*ctg(300)=frac{sin(-60)}{cos(-60)}*frac{cos(300)}{sin(300)} \ cos(300)=cos(240+60)=cos240cos60-sin240sin60=(-frac{sqrt{3}}{2}*frac{1}{2})-(-frac{1}{2}*frac{sqrt{3}}{2})=1 \ sin(300)=sin(240+60)=sin240cos60+sin60cos240=(-frac{sqrt{3}}{2}*frac{1}{2})+(frac{sqrt{3}}{2}*(-frac{1}{2})=-frac{sqrt{3}}{2} \ frac{1}{frac{-sqrt{3}}{2}}=frac{2}{-sqrt{3}} \ frac{sin(-60)}{cos(-60)}=frac{sqrt{3}}{2}*(-frac{1}{2})=-frac{sqrt{3}}{4} \ (-frac{sqrt{3}}{4})*(-frac{2}{sqrt{3}})=1/2$

2)

$frac{6}{x+1}=frac{2}{x}+1 \ frac{6}{x+1}=frac{2+x}{x} \ 6x=(x+1)(2+x) \ 6x=2x+x^{2}+2+x \ x^{2}-3x+2=0 \ x_{1}=2 x_{2}=1$

3)

$log_{9}3x+log_{9}1=log_{9}x \ log_{9}3x-log_{9}x=-log_{9}1 \ log_{9}3=-log_{9}1 \ 3neq0$