已知cos(x+π/6)=5/13,x∈(0,π/2),则cosx=

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/07 03:27:10
已知cos(x+π/6)=5/13,x∈(0,π/2),则cosx=

已知cos(x+π/6)=5/13,x∈(0,π/2),则cosx=
已知cos(x+π/6)=5/13,x∈(0,π/2),则cosx=

已知cos(x+π/6)=5/13,x∈(0,π/2),则cosx=
x∈(0,π/2)
x+π/6∈(π/6,2π/3)
所以sin(x+π/6)>0
sin²(x+π/6)+cos²(x+π/6)=1
所以sin(x+π/6)=12/13
cosa
=cos[(x+π/6)-π/6]
=cos(x+π/6)cosπ/6+sin(x+π/6)sinπ/6
=(5√3+12)/26