2. Решите неравенство методом интервалов: а) (х -12)(х + 11) < 0 б) (х + 1,7)(х – 9) (4,2 +х) < 0 в) (6х + 1)(х – 14) < 0 г) (2x – 3)(х + 4) > 0) 6-х г) > 0 x - 11

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