已知0<a<兀/2,cos(a+兀/6)=3/5,求cosa?

问题描述:

已知0<a<兀/2,cos(a+兀/6)=3/5,求cosa?

因为 0从而 sin(a+π/6)>0
于是 sin(a+π/6)=√[1-cos(a+π/6)]=4/5
所以
cosa=cos[(a+π/6)-π/6)]
=cos(a+π/6)·cos(π/6)+sin(a+π/6)·sin(π/6)
=(4+3√3)/10