Question

Алгебра 10 класс) Помогите с № 30

Answer 1

$1)quad frac{tgfrac{pi}{8}}{1-tg^2frac{pi}{8}}=[; tg2a= frac{2tga}{1-tg^2a} ; frac{tga}{1-tg^2a}=frac{1}{2}tg2a]=frac{1}{2}tgfrac{pi}{4}=frac{1}{2}cdot 1=frac{1}{2}\\2)quad frac{1-tg^2frac{pi}{12}}{1+tg^2frac{pi}{12}} =left [cosa= frac{1-tg^2frac{a}{2}}{1+tg^2frac{a}{2}}right ]= cosfrac{pi}{6}=frac{sqrt3}{2}$

$3)quad frac{tgfrac{pi}{8}}{1+tg^2frac{pi}{8}} =frac{1}{2}sin(2cdot frac{pi}{8})=frac{1}{2}cdot sinfrac{pi}{4}=frac{1}{2}cdot frac{sqrt2}{2}=frac{sqrt2}{4}$

$4)quad frac{sin25cdot sin65}{cos40} = frac{sin25cdot sin(90-25)}{cos40} = frac{sin25cdot cos25}{cos40} = frac{frac{1}{2}sin50}{cos(90-50)}=\\= frac{sin50}{2sin50} = frac{1}{2}\\5)quad (cos^210-cos ^280)^2+cos^270=\\=(cos^210-cos^2(90-10))^2+cos^270=\\=(cos^210-sin^210)^2+cos^270=cos^220+cos^2(90-20)=\\=cos^220+sin^220=1$

Answer 2

Большое спасибо!