5+ lg² x= -4lgx
5+lg²x+4lgx=0
Пусть lgx=t, тогда lg²x=t².
5+t²+4t=0
t²+4t+5=0
t₁= -5 t₂=1
Делаем обратную замену.
lgx= -5 lgx=1
x=1/10⁵ x=10
1) cos a cos 3a - sin a sin 3a = cos (a+3a) = cos 4a
2) sin 2a cos a + cos 2a sin a = sin (2a+a) = sin 3a
3) sin40°cos5°+cos40°sin5° = sin(40°+5°)= sin 45° = ![\frac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=+%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D+++)
4) ![\dfrac{tg\frac{7\pi}{15}-tg\frac{2\pi}{15}}{1+tg\frac{7\pi}{15}tg\frac{2\pi}{15}} = tg(\frac{7\pi}{15}-\frac{2\pi}{15}) =tg\frac{5\pi}{15}=tg\frac{\pi}{3}=\sqrt{3}](https://tex.z-dn.net/?f=+%5Cdfrac%7Btg%5Cfrac%7B7%5Cpi%7D%7B15%7D-tg%5Cfrac%7B2%5Cpi%7D%7B15%7D%7D%7B1%2Btg%5Cfrac%7B7%5Cpi%7D%7B15%7Dtg%5Cfrac%7B2%5Cpi%7D%7B15%7D%7D++%3D+tg%28%5Cfrac%7B7%5Cpi%7D%7B15%7D-%5Cfrac%7B2%5Cpi%7D%7B15%7D%29+%3Dtg%5Cfrac%7B5%5Cpi%7D%7B15%7D%3Dtg%5Cfrac%7B%5Cpi%7D%7B3%7D%3D%5Csqrt%7B3%7D++)
5) ![\pi <\alpha <\frac{3\pi}{2} => cos \alpha <0](https://tex.z-dn.net/?f=+%5Cpi+%3C%5Calpha+%3C%5Cfrac%7B3%5Cpi%7D%7B2%7D++%3D%3E+cos+%5Calpha+%3C0+)
![sin^2\alpha +cos^2\alpha =1\\ cos\alpha =-\sqrt{1-(\frac{4}{5})^2} =-\sqrt{1-\frac{16}{25}}=-\sqrt{\frac{9}{25}}=-\frac{3}{5}](https://tex.z-dn.net/?f=+sin%5E2%5Calpha+%2Bcos%5E2%5Calpha+%3D1%5C%5C+cos%5Calpha+%3D-%5Csqrt%7B1-%28%5Cfrac%7B4%7D%7B5%7D%29%5E2%7D++%3D-%5Csqrt%7B1-%5Cfrac%7B16%7D%7B25%7D%7D%3D-%5Csqrt%7B%5Cfrac%7B9%7D%7B25%7D%7D%3D-%5Cfrac%7B3%7D%7B5%7D++++++)
4(3-t)<6(1/3-t)
2t<-10
t<-5
12+20<2+30
32<32
Неравенство не верное.
32=32
1) f(x)=5cos²x-3
f `(x)=-5sin2x
f `(п/6) = -5sin2*п/6= (-5√3)/2
2) f(x)=-sinx+x
f `(x)=-cosx+1
f `(0)=-cos(0)+1=0