tg20°*tg40°*tg60°*tg80°=
=tg20°*(tg60-20°)*tg60°*tg(60°+20°)=
= [tg20°*tg(60°-20°)tg(60°+20°)]*tg60°=
=[tg20°*((sin60°-20°)*sin(60°+20°)/(cos(60°-20°)cos(60°+20°))]*√3 =
=[tg20°*(√3/2 *cos20° -1/2 * sin20°)(√3/2 *cos20° +1/2 * sin20°) :
(1/2*cos20°+√3/2 *sin20°)(1/2*cos20°-√3/2 *sin20°)]*√3 =
=[tg20°*(3/4*cos²20°-1/4sin²20°)/(1/4*cos20°-3/4sin20°)]*√3 =
=[(sin20°/cos20°)*(3cos²20°-sin²20°)/(cos²20°-3sin²20°)]*√3=
=[(3cos²20°*sin20°-sin³20°)/(cos³20°-3sin²20°cos20°)]*√3=
=(sin3*20°)/cos(3*20°)*√3= (sin60°)/(cos60°)*√3 = tg60°*√3 =√3*√3=3
1) 5b² + (3 - 2b)(3 + 2b) = 5b² + 9 - 4b² = b² + 9
2) x³ - 27 = (x - 3)(x² + 3x + 9)
3)
![( \frac{ \sqrt[3]{9 \sqrt{3} } }{ \sqrt{3 \sqrt[3]{3} } } )^3=\frac{{9 \sqrt{3}} }{ (\sqrt{3^{ \frac{4}{3}} })^3 } =\frac{{9 \sqrt{3}} }{ \sqrt{3^4}} =\frac{{9 \sqrt{3}} }{ 9} = \sqrt{3}](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%20%5Csqrt%5B3%5D%7B9%20%5Csqrt%7B3%7D%20%7D%20%7D%7B%20%5Csqrt%7B3%20%5Csqrt%5B3%5D%7B3%7D%20%7D%20%7D%20%29%5E3%3D%5Cfrac%7B%7B9%20%5Csqrt%7B3%7D%7D%20%7D%7B%20%28%5Csqrt%7B3%5E%7B%20%5Cfrac%7B4%7D%7B3%7D%7D%20%7D%29%5E3%20%7D%20%3D%5Cfrac%7B%7B9%20%5Csqrt%7B3%7D%7D%20%7D%7B%20%5Csqrt%7B3%5E4%7D%7D%20%3D%5Cfrac%7B%7B9%20%5Csqrt%7B3%7D%7D%20%7D%7B%209%7D%20%3D%20%5Csqrt%7B3%7D%20)
4)
![(1+c^{\frac{1}{2} )^{2}](https://tex.z-dn.net/?f=%281%2Bc%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%29%5E%7B2%7D)
![- 2c^{\frac{1}{2}}=1+2c^{\frac{1}{2}} + c- 2c^{\frac{1}{2}}=1+c](https://tex.z-dn.net/?f=%20-%202c%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D1%2B2c%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%2B%20c-%202c%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D1%2Bc)
5)
![\left \{ {{b_3+b_4=36} \atop {b_2+b_3=18}} \right. \\ \\ \left \{ {{q(b_2+b_3)=36} \atop {b_2+b_3=18}} \right. \\ \\ \left \{ {{q=2} \atop {b_1q(1+q)=18}} \right. \\ \\ \left \{ {{q=2} \atop {b_1=3}} \right. \\ b_5=b_1q^4=3*2^4=48](https://tex.z-dn.net/?f=%20%5Cleft%20%5C%7B%20%7B%7Bb_3%2Bb_4%3D36%7D%20%5Catop%20%7Bb_2%2Bb_3%3D18%7D%7D%20%5Cright.%20%5C%5C%20%20%5C%5C%20%20%5Cleft%20%5C%7B%20%7B%7Bq%28b_2%2Bb_3%29%3D36%7D%20%5Catop%20%7Bb_2%2Bb_3%3D18%7D%7D%20%5Cright.%20%20%20%5C%5C%20%20%5C%5C%20%20%5Cleft%20%5C%7B%20%7B%7Bq%3D2%7D%20%5Catop%20%7Bb_1q%281%2Bq%29%3D18%7D%7D%20%5Cright.%20%5C%5C%20%20%5C%5C%20%20%20%5Cleft%20%5C%7B%20%7B%7Bq%3D2%7D%20%5Catop%20%7Bb_1%3D3%7D%7D%20%5Cright.%20%5C%5C%20b_5%3Db_1q%5E4%3D3%2A2%5E4%3D48)
Ответ в приложенном фото)
(5/х4)1= 5/х4
Любое выражение возведённое в степень 1, равно самому себе