A)sin2*75=sin150=1/2
b)sin π/4 = √2/2
c) 1/2 sin30 = 1/2 * 1/2=1/4
d)cos² π/8+sin² π/8 +2sin π/8cosπ/8 = 1+sinπ/4 = 1+ √2/2
e)sin² π/12 +cos²π/12 -2sin π/12cos<span>π/12= 1-sin </span>π/6 = 1-1/2=1/2
f)cos2*75 = cos 150=1/2
g)cos π/4 = √2/2
h)1-cos² π/12 - cos² π/12 = sin² π/12 - cos ² π/12 = -cos π/6= -√3/2
По формуле бинома Ньютона
![(2x-y)^5=\displaystyle \sum^{5}_{k=0}C^k_5\cdot (2x)^{5-k}\cdot (-y)^k](https://tex.z-dn.net/?f=%282x-y%29%5E5%3D%5Cdisplaystyle%20%5Csum%5E%7B5%7D_%7Bk%3D0%7DC%5Ek_5%5Ccdot%20%282x%29%5E%7B5-k%7D%5Ccdot%20%28-y%29%5Ek)
Найдем второй и четвертый член разложения при k = 1 и k = 3![a_2=C^1_{5}\cdot (2x)^{5-1}\cdot (-y)^1=-5\cdot 16x^4y=-80x^4y\\ \\ a_4=C^3_5\cdot (2x)^{5-3}\cdot (-y)^3=\dfrac{5!}{3!2!}\cdot 4x^2\cdot (-y^3)=-40x^2y^3](https://tex.z-dn.net/?f=a_2%3DC%5E1_%7B5%7D%5Ccdot%20%282x%29%5E%7B5-1%7D%5Ccdot%20%28-y%29%5E1%3D-5%5Ccdot%2016x%5E4y%3D-80x%5E4y%5C%5C%20%5C%5C%20a_4%3DC%5E3_5%5Ccdot%20%282x%29%5E%7B5-3%7D%5Ccdot%20%28-y%29%5E3%3D%5Cdfrac%7B5%21%7D%7B3%212%21%7D%5Ccdot%204x%5E2%5Ccdot%20%28-y%5E3%29%3D-40x%5E2y%5E3)
Ответ:
........ Интересно, с чем?
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