Х³-х=0
х(х²-1)=0
х=0
или
х²-1=0
х²=1
х=1; х=-1
ответ: -1; 0; 1
х²-24х+144=0
(х-12)²=0
х-12=0
х=12
ответ: 12
25у²-49=0
25у²=49
у²=49/25
у=7/5; у=-7/5
ответ: -7/5; 7/5
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++++++)