sin(a-b)=√10/10，0<b<90度，求cosb的值(sina=2√5/5，cosa=√5/5)

显示全部楼层 · 2011-12-24 16:33:33

由sina=2√5/5，cosa=√5/5得出00.sin(a-b)=√10/10得cos(a-b)=±3√10/10。而cosb=cos[a-(a-b)]=cosacos(a-b)+sinasin(a-b)=√5/5*(±3√10/10)+2√5/5*√10/10=(2±3)√50/50显然只能取加号，否则为负值。于是cosb=(2+3)√50/50=√2/2，b=...

千问 · 2011-12-24 16:33:33

sinacosb-cosasinb=√10/10(2√5/5)cosb-(√5/5)sinb=√10/102cosb-sinb=√2/22cosb-√2/2=sinb4cos(^2)b-2√2cosb+1/2=1-cos(^2)b3cos(^2)b-2√2cosb-1/2=0cosb=(2√2+√14)/6...