arccot（2加上根号2加上根号3加上根号6），要用弧度制表示的值

更新时间2022-03-19 21:26:02

arccot（2+√2+√3+√6）=

2+√2+√3+√6

=(2+√2)+(√3+√6)

=(√2+1)√2+(1+√2)√3

=(√2+1)(√2+√3)

=(1+√2)/(√3-√2)

=(0.5+0.5√2)/(0.5√3-0.5√2)

=[cos(π/3)+cos(π/4)]/[sin(π/3)-sin(π/4)]

=2cos(π/6+π/8)cos(π/6-π/8)

   /[2cos(π/6+π/8)sin(π/6-π/8)]

=cos(π/6-π/8)/sin(π/6-π/8)

=cos(π/24)/sin(π/24)

=cot(π/24)

∴ arc cot(2+√2+√3+√6)=π/24