Задача 28041 ...
Условие
вторая задача
cos(-π/3)ctg(-7π/4)+sin 2π/3 tg(-5π/6)
математика
2776
Решение
★
Все решения
tg(–7π/4)=tg((π/4)-2π)= - (tg(2π)-(π/4))= - (-tg(π/4))=1
sin(7π/6)=sin(π+(π/6))=- sin(π/6)=-1/2
cos(–π)=-1
tg(–π/4)=-1
cos π/4 tg(–7π/4)–sin(7π/6) cos(–π)tg(–π/4)=
=(sqrt(2)/2)+(1/2)=(sqrt(2)+1)/2
вторая задача
cos(–π/3)=cos(π/3)= 1/2
ctg(–7π/4)=ctg((π/4)-2π)= - (ctg(2π)-(π/4))= - (-ctg(π/4))=1
sin (2π/3)=sqrt(3)/2
tg(–5π/6) =-tg(5π/6) =-tg(π-(π/6))=-(-tg( π/6))=sqrt(3)/3
cos(–π/3)ctg(–7π/4)+sin 2π/3 tg(–5π/6)=(1/2)+(3/6)=1