化简sin(kπ+a)+sin(a-kπ)除以sin(a+Kπ)cos(a-Kπ).(kEZ)
问题描述:
化简sin(kπ+a)+sin(a-kπ)除以sin(a+Kπ)cos(a-Kπ).(kEZ)
答
当k为偶数时sin(kπ+a)=sina,sin(a-kπ)=sina,
cos(a-Kπ)=cosa
sin(kπ+a)+sin(a-kπ)除以sin(a+Kπ)cos(a-Kπ)
=2sina/sinacosa=2/cosa;
当k为奇数时sin(kπ+a)=-sina,sin(a-kπ)=-sina,
cos(a-Kπ)=-cosa
sin(kπ+a)+sin(a-kπ)除以sin(a+Kπ)cos(a-Kπ)
=-2sina/sinacosa=-2/cosa;