Question

cos 135°cos 105° помагите

Answer 1

$displaystyle cos135^{circ}cos105^{circ}= frac{1}{2}(cos(135+105)+cos(135-105))=frac{1}{2}(cos240^{circ}+$
$displaystyle +cos30^{circ})= frac{1}{2}(cos(270^{circ}-30^{circ})+cos30^{circ})= frac{1}{2}(-sin30^{circ}+ frac{ sqrt3}{2})=$$displaystyle = frac{1}{2}(-frac{1}{2}+ frac{ sqrt3}{2})= boxed{frac{ sqrt 3-1}{4}}$