Question

ПОМОГИТЕ ПОЖАЛУЙСТА. 1 и 2

Answer 1

1. sinα=1/2, 0<α<π/2, ⇒ α=π/6
√3tgα+ctg²α-4cos2α=√3tg(π/6)+ctg²(π/6)-4cos(π/3)=√3*√3/3+(√3)²-4*1/2=
=3/3+3-2=1+3-2=2.

$2. ( frac{9}{2} )^{x+4} geq ( frac{4}{81})^{3+x}; \ ( frac{9}{2})^{x+4} geq ( frac{9}{2})^{-2(3+x)}; \ x+4 geq -2(3+x); \ x+4 geq -6-2x; \ x+2x geq -4-6; \ 3x geq -10; \ x geq - frac{10}{3};$
Ответ: [-10/3;+∞).