Вычислить lim (1-sin x/2)/ cosx/2(cosx/4-sinx/4) - вопрос №184968312244 от moudoder 05.02.2020 15:28

Question

Математика: Вычислить lim (1-sin x/2)/ cosx/2(cosx/4-sinx/4) ..x стремится к pi

moudoder · Answer

lim (1-sin x/2)/ (cosx/2(cosx/4-sinx/4))=lim(cos^2(x/4)-2sin(x/4)cos(x/4)+sin^2(x/4))/ (cosx/2(cosx/4-sinx/4))=lim (cos(x/4)-sin(x/4))^2/ (cosx/2(cosx/4-sinx/4))=lim (cos(x/4)-sin(x/4))/ (cosx/2)=lim (cos(x/4)-sin(x/4))/ (cos^2(x/4)-sin^2(x/4))=lim (cos(x/4)-sin(x/4))/ ((cos(x/4)-sin(x/4))(cos(x/4)+sin(x/4))=lim (1/ ((cos(x/4)+sin(x/4)))=1/(K(2)/2+K(2)/2)=1/K(2)=K(2)/2...