Question

HEEEELP, тригонометрия((
1. Sin49*Sin11+Cos^2 (71)+1 (ответ: 1.25)
2. Sinx-Cosx=7/5, найти tg(x/2), если 0<tg(x/2)<3
 

Answer 1

1)
$sin49sin11+cos^2(71)+1\ sin(30+19)sin(30-19)+cos^2(90-19)+1\ sin^2(30)cos^2(19)-cos^2(30)*sin^2(19)+sin^219+1\ sin^2(30)cos^2(19)-sin^2(19)(cos^2(30)-1)+1\ sin^2(30)cos^2(19)+sin^2(19)sin^2(30)+1\ sin^2(30)+1=frac{1}{4}+1=1.25$

2) 
$sinx-cosx=frac{7}{5}\ tg(frac{x}{2})=frac{sinx}{1+cosx}\ sinx-sqrt{1-sin^2x}=frac{7}{5}\ 1-sin^2x=(sinx-frac{7}{5})^2\ 1-sin^2x= frac{25sin^2x-70sinx+49}{25}\ 25-25sin^2x=25sin^2x-70sinx+49\ 50sin^2x-70sinx+24=0\ sinx=frac{3}{5}\ sinx=frac{4}{5}$
$tg(frac{frac{3}{5}}{2})=frac{sin(arcsinfrac{3}{5})}{1+cos(arcsinfrac{3}{5})}=frac{frac{3}{5}}{1+frac{4}{5}}=frac{1}{3}$

Вторую так же и выйдет 0,5