已知x∈(0,/4),且sin(π/4-x)=5/13.求cos2x/cos(π/4 + x)的值
问题描述:
已知x∈(0,/4),且sin(π/4-x)=5/13.求cos2x/cos(π/4 + x)的值
答
sin(π/4-x)=5/13 ,√2/2(cosx-sinx)=5/13
(cosx-sinx)=5√2/13 ,1-sin2x=50/169
sin2x=119/169 ,cos2x=161.4/169
cos(π/4 + x)=cos[π/2-(π/4 - x)]
=sin(π/4-x)=5/13
cos2x/cos(π/4 + x)=161.4/169*13/5
=161.4/65