已知cos(π/4+x)=5/13,0＜x＜π/4,求sin(π/4-x)/cos2x超急的!
问题描述：
已知cos(π/4+x)=5/13,0＜x＜π/4,求sin(π/4-x)/cos2x
超急的!
答
因为π/4+x和π/4-x是互余的（和是π/2）,
所以cos(π/4+x）=sin(π/4-x)=5/13
因为0＜x＜π/4
所以sin(π/4+x)=12/13 (因为π/4+x为第一象限角)
cos2x=sin(π/2+2x)
=2*sin(π/4+x)*cos(π/4+x)
=2×(5/13)×(12/13)
=120/169
所以sin(π/4-x)/cos2x
=(5/13)/(120/169)
=13/24