已知0<α<π/4,sin(α+π/4)=3/5,求cosα.
问题描述:
已知0<α<π/4,sin(α+π/4)=3/5,求cosα.
答
0<α<π/4
则π/4<α+π/4<π/2
∴cos(α + π/4)>0
∴cos(α + π/4)=4/5
cosα
=cos[(α + π/4) - π/4]
=cos(α + π/4)cosπ/4 + sin(α + π/4)sinπ/4
=(4/5)×(√2/2) + (3/5)×(√2/2)
=(7/10)√2