Question

Hlp, тригонометрия(( 1. sin49*sin11+cos^2 (71)+1 (ответ: 1.25) 2. sinx-cosx=7/5, найти tg(x/2), если 0

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

Вторую так же и выйдет 0,5