计算：1除以cos(24分之5π)，(答案要用带根号的)

更新时间2022-01-19 00:39:27

1÷cos(5π/24)=

以上解答满意了么，这里只是给出解题思路，根式计算比较复杂，结果是否准确，请你自己仔细再计算一下

1÷cos(5π/24)=1/sin(π/2-5π/24)

=1/sin(7π/24)=1/sin(π/6+π/8)

=1/[sin(π/6)cos(π/8)+cos(π/6)sin(π/8)]

=1/[0.5*0.5√(2+√2)+0.5√3*0.5√(2-√2)]

=4/[√(2+√2)+√(6-3√2)]

=4[√(2+√2)-√(6-3√2)]/[(2+√2)-(6-3√2)]

=[√(2+√2)-√(6-3√2)]/(√2-1)

=(√2+1)[√(2+√2)-√6-3√2)]

=(√√2)√(√2+1){√[(√2+1)(√2+1)]-√[(√2+1)*(3√2-3)]}

=√(2+√2)*(√2+1-√3)

.

sin(π/6)=0.5，cos(π/6)=0.5√3，cos(π/4)=0.5√2

sin(π/8)=√{0.5[1-cos(π/4)]}=0.5√(2-√2)

cos(π/8)√{0.5[1+cos(π/4)]}=0.5√(2+√2)