Предмет: Алгебра,
автор: Rose21
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
Ответы
Автор ответа:
0
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](https://tex.z-dn.net/?f=sin49sin11%2Bcos%5E2%2871%29%2B1%5C%0Asin%2830%2B19%29sin%2830-19%29%2Bcos%5E2%2890-19%29%2B1%5C%0Asin%5E2%2830%29cos%5E2%2819%29-cos%5E2%2830%29%2Asin%5E2%2819%29%2Bsin%5E219%2B1%5C%0Asin%5E2%2830%29cos%5E2%2819%29-sin%5E2%2819%29%28cos%5E2%2830%29-1%29%2B1%5C%0Asin%5E2%2830%29cos%5E2%2819%29%2Bsin%5E2%2819%29sin%5E2%2830%29%2B1%5C%0Asin%5E2%2830%29%2B1%3Dfrac%7B1%7D%7B4%7D%2B1%3D1.25%0A "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}\](https://tex.z-dn.net/?f=sinx-cosx%3Dfrac%7B7%7D%7B5%7D%5C%0Atg%28frac%7Bx%7D%7B2%7D%29%3Dfrac%7Bsinx%7D%7B1%2Bcosx%7D%5C%0Asinx-sqrt%7B1-sin%5E2x%7D%3Dfrac%7B7%7D%7B5%7D%5C%0A1-sin%5E2x%3D%28sinx-frac%7B7%7D%7B5%7D%29%5E2%5C%0A1-sin%5E2x%3D+frac%7B25sin%5E2x-70sinx%2B49%7D%7B25%7D%5C%0A25-25sin%5E2x%3D25sin%5E2x-70sinx%2B49%5C%0A50sin%5E2x-70sinx%2B24%3D0%5C+sinx%3Dfrac%7B3%7D%7B5%7D%5C%0Asinx%3Dfrac%7B4%7D%7B5%7D%5C%0A "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}\](https://tex.z-dn.net/?f=+tg%28frac%7Bfrac%7B3%7D%7B5%7D%7D%7B2%7D%29%3Dfrac%7Bsin%28arcsinfrac%7B3%7D%7B5%7D%29%7D%7B1%2Bcos%28arcsinfrac%7B3%7D%7B5%7D%29%7D%3Dfrac%7Bfrac%7B3%7D%7B5%7D%7D%7B1%2Bfrac%7B4%7D%7B5%7D%7D%3Dfrac%7B1%7D%7B3%7D%5C%0A "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
2)
Вторую так же и выйдет 0,5
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