І - 0,3х
ІІ -0,3х*5/6=0,25х (л) }
ІІІ - 0,3х-26(л) } x л
ІV - 0,25х+10(л)
0,3х+0,25х+0,3х-26+0,25х10=х
0,1х=16
х=160(л) - всего
160*0,3=48(л) - в І бидоне
160*0,25=40(л) - во ІІ бидоне
48-26=22(л) - в ІІІ бидоне
40+10=50(л) - в ІV бидоне
Проверка:
48+22+40+50=160(л)
Sin²α-1= sin²α-(sin²α+cos²α)= sin²α-sin²α-cos²α= - cos²α
(sinα+cosα)²+(sinα-cosα)²= sin²α+2sinαcosα+cos²α+sin²α-2sinαcosα+cos²α= 2
<span>1) (1+ ctg</span>β<span>)</span>²<span>+ (1 - ctg</span>β<span> )</span>²=1+2ctgβ+ctg²β+1-2ctgβ+ctg²β=
=2+2ctg²β=2(1+ctg²β)=1/sin²β;<span>
2) </span>
![tgx+ \frac{cosx}{1+sinx} = \frac{tgx(1+sinx)+cosx}{1+sinx} = \frac{tgx+ \frac{sin ^{2}x }{cosx}+cosx }{1+sinx}= \frac{sinx+sin ^{2}x+cos^{2}x}{cosx}* \\ * \frac{1}{1+sinx}= \frac{1+sinx}{cosx} * \frac{1}{1+sinx}= \frac{1}{cosx}; \\](https://tex.z-dn.net/?f=tgx%2B+%5Cfrac%7Bcosx%7D%7B1%2Bsinx%7D+%3D+%5Cfrac%7Btgx%281%2Bsinx%29%2Bcosx%7D%7B1%2Bsinx%7D+%3D+%5Cfrac%7Btgx%2B+%5Cfrac%7Bsin+%5E%7B2%7Dx+%7D%7Bcosx%7D%2Bcosx+%7D%7B1%2Bsinx%7D%3D+%5Cfrac%7Bsinx%2Bsin+%5E%7B2%7Dx%2Bcos%5E%7B2%7Dx%7D%7Bcosx%7D%2A+%5C%5C+%2A+%5Cfrac%7B1%7D%7B1%2Bsinx%7D%3D+%5Cfrac%7B1%2Bsinx%7D%7Bcosx%7D+%2A+%5Cfrac%7B1%7D%7B1%2Bsinx%7D%3D+%5Cfrac%7B1%7D%7Bcosx%7D%3B+%5C%5C+++++)
<span>
3) </span>
![\frac{cos \beta }{1-sin \beta}+ \frac{1-sin \beta }{cos \beta }= \frac{cos^{2} \beta +1-2sin \beta +sin^{2} \beta }{(1-sin \beta )cos \beta } = \frac{2(1-sin \beta )}{(1-sin \beta )cos \beta }= \frac{2}{cos \beta };](https://tex.z-dn.net/?f=+%5Cfrac%7Bcos+%5Cbeta+%7D%7B1-sin+%5Cbeta%7D%2B+%5Cfrac%7B1-sin+%5Cbeta+%7D%7Bcos+%5Cbeta+%7D%3D+%5Cfrac%7Bcos%5E%7B2%7D+%5Cbeta++%2B1-2sin+%5Cbeta+%2Bsin%5E%7B2%7D++%5Cbeta+%7D%7B%281-sin+%5Cbeta+%29cos+%5Cbeta+%7D++%3D+%5Cfrac%7B2%281-sin+%5Cbeta+%29%7D%7B%281-sin+%5Cbeta+%29cos+%5Cbeta+%7D%3D+%5Cfrac%7B2%7D%7Bcos+%5Cbeta+%7D%3B+++)
<span>
4) </span>
![\frac{1+tg \alpha }{1+ctg \alpha } = \frac{cos \alpha+sin \alpha }{cos \alpha } * \frac{sin \alpha }{sin \alpha +cos \alpha }= \frac{sin \alpha }{cos \alpha } =tg \alpha .](https://tex.z-dn.net/?f=+%5Cfrac%7B1%2Btg+%5Calpha+%7D%7B1%2Bctg+%5Calpha+%7D+%3D+%5Cfrac%7Bcos+%5Calpha%2Bsin+%5Calpha++%7D%7Bcos+%5Calpha+%7D+%2A+%5Cfrac%7Bsin+%5Calpha+%7D%7Bsin+%5Calpha+%2Bcos+%5Calpha+%7D%3D+%5Cfrac%7Bsin+%5Calpha+%7D%7Bcos+%5Calpha+%7D+%3Dtg+%5Calpha+.+)