<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+++++)
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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+++)
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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+.+)
(3^11*3^3)/(3^2)^6= (3^11+3)/3^12=3^14/3^12= 3^14-12= 3^2=9
2,5*19 - 9*2,5 - 0,25*31*4 = 47,5 - 22,5 - 31 = -6
Производную найди, приравняй ее к нулю и полученные иксы будут точками экстремума
3sinx-4cosx=5
3sinx+4cosx= -5 Делим на 5
3/5sinx+4/5cosx=-1
sin(x+ arcsin4/5) = -1
x+arcsin4/5 = -pi/2+2pi*k
x= -pi/2+2pi*k - arcsin4/5