x∈(0,π/4)cos(π/4+x)=5/13 则cos2x=

问题描述:

x∈(0,π/4)cos(π/4+x)=5/13 则cos2x=
RT

π/4+x属于(π/4,π/2)
sin(π/4+x)>0
sin²+cos²=1
所以sin(π/4+x)=12/13
所以2sin(π/4+x)cos(π/4+x)=120/169
sin(π/2+2x)=120/169
cos(2x)=120/169