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
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
Найдите производные функций
а) y=4x
y` = 4
б) y=2√x+3sin2x
y` = 2/(2√x) + 3 * 2* cos2x = 1/√x + 6*cos2x
в) y=x*cosx
y` = (x)` * cosx + x * (cosx)` = cosx - x*sinx
г) y=tg²x
y` = 2tgx * (1 / cos²x) = (2*sinx) / cos³x
д) y=(3x+5)/4 = 3x / 4 + 5/4
y` = (3/4) * x + 5/4)` = 3/4 + 0 = 3/4