Question

27 БАЛЛОВ СРОЧНО!!!!

Answer 1

$7); ; frac{4}{sqrt3}cdot sin(-420^circ )=-frac{4}{sqrt3}cdot sin(360^circ +60^circ )=-frac{4}{sqrt3}cdot sin60^circ =\\=-frac{4}{sqrt3}cdot frac{sqrt3}{2}=-2\\\8); ; (cosfrac{3pi}{8}-sinfrac{3pi}{8})(cosfrac{3pi}{8}+sinfrac{3pi}{8})=cos^2frac{3pi}{8}-sin^2frac{3pi}{8}=\\=cosfrac{3pi}{4}=cos(pi -frac{pi}{4})=-cosfrac{pi}{4}=-frac{sqrt2}{2}$

$9); ; frac{sin40^circ}{sin20^circ }=frac{2cdot sin20^circ cdot cos20^circ }{sin20^circ }=2cdot cos20^circ$

$10); ; -4(sin^270^circ +sin^2160^circ )=-4, Big(frac{1-cos140^circ }{2}+frac{1-cos320^circ }{2}Big)=\\=-4cdot frac{1-cos(180^circ -40^circ )+1-cos(360^circ -40^circ )}{2}=\\=-2cdot Big(2+cos40^circ -cos40^circ Big)=-2cdot 2=-4$