Кос 60 градусов= 1:2
sin ^4 a= (sin^2a)^2 = (sin^2a)(sin^2a)
tg 45=1
a^2-b^2=(a+b)(a-b)
sin^4a-cos^4a= (sin^2a+cos^2a) (sin^2a-cos^2a ) + cos ^2 a
____sin^2a+cos^2a= 1
_sin^2a-cos^2a + cos ^2 a=sin^2a/ 1/2= 2 * sin ^2 a
znanija.com/task/314934 этот вопрос решали
![\displaystyle \frac{6 cos^2x-5 \sqrt{2} cosx+2}{lg(tgx)}=0](https://tex.z-dn.net/?f=%5Cdisplaystyle++%5Cfrac%7B6+cos%5E2x-5+%5Csqrt%7B2%7D+cosx%2B2%7D%7Blg%28tgx%29%7D%3D0+)
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дробь равна нулю когда числитель равен нулю
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![\displaystyle cosx= \frac{ \sqrt{2}}{2}\\\\x_{1.2}=\pm \frac{ \pi }{4}+2 \pi n; n\in Z\\\\x_1= \frac{ \pi }{4}+2 \pi n; n\in Z](https://tex.z-dn.net/?f=%5Cdisplaystyle+cosx%3D++%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B2%7D%5C%5C%5C%5Cx_%7B1.2%7D%3D%5Cpm++%5Cfrac%7B+%5Cpi+%7D%7B4%7D%2B2+%5Cpi+n%3B+n%5Cin+Z%5C%5C%5C%5Cx_1%3D+%5Cfrac%7B+%5Cpi+%7D%7B4%7D%2B2+%5Cpi+n%3B+n%5Cin+Z+++++)
не входит в ОДЗ
![\displaystyle x_2=- \frac{ \pi }{4}+2 \pi n; n\in z](https://tex.z-dn.net/?f=%5Cdisplaystyle+x_2%3D-+%5Cfrac%7B+%5Cpi+%7D%7B4%7D%2B2+%5Cpi+n%3B+n%5Cin+z+)
не входит в ОДЗ
![\displaystyle cosx= \frac{ \sqrt{2}}{3}\\\\x_{3.4}=\pm arccos( \frac{ \sqrt{2}}{3})+2 \pi n; n\in Z\\\\x_3=- arccos( \frac{ \sqrt{2}}{3})+2 \pi n; n\in Z](https://tex.z-dn.net/?f=%5Cdisplaystyle+cosx%3D+%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B3%7D%5C%5C%5C%5Cx_%7B3.4%7D%3D%5Cpm+arccos%28+%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B3%7D%29%2B2+%5Cpi+n%3B+n%5Cin+Z%5C%5C%5C%5Cx_3%3D-+arccos%28+%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B3%7D%29%2B2+%5Cpi+n%3B+n%5Cin+Z+++)
не входит в ОДЗ
ОТВЕТ
![\displaystyle x_4=arccos \frac{ \sqrt{2}}{3}+2 \pi n; n\in Z](https://tex.z-dn.net/?f=%5Cdisplaystyle+x_4%3Darccos++%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B3%7D%2B2+%5Cpi+n%3B+n%5Cin+Z+)
cos4a-2sin2acos2a*cos2a/sin2a= cos4a-2cos²2a=cos²2a-sin²2a-2cos²2a=-sin²2a-cos²2a=-(sin²2a+cos²2a)=-1 тождество верно
ctg 315= ctg(360-45)=-ctg45=-1
3/2sint(если sin в числители);1+2sin^2t/2(если sin в знаменатели)
Cos²(α)=1-sin²(α)=1-1/9=8/9. А так как угол α лежит во 2 четверти, то cos(α)<0. Тогда cos(α)=-√8/9=-2*√2/3. tg(α/2)=(1-cos(α))/sin(α)=3+2*√2.
Вывод формулы для tg(α/2).
tg(α/2)=sin(α/2)/cos(α/2), cos(α)=cos²(α/2)-sin²(α/2), 1-cos(α)=sin²(α/2)+cos²(α/2)-((cos²(α/2)-sin²(α/2))=2*sin²(α/2), sin(α)=2*sin(α/2)*cos(α/2). Тогда (1-cos(α))/sin(α)=sin(α/2)/cos(α/2)=tg(α/2)