tan(5π/24)，等于多少

更新时间2022-01-19 01:07:52

求(5π/24)的正切值，答案要用带根号的

【11】

sin(5π/12)=sin(π/4+π/6)

=sin(π/4)cos(π/6)+cos(π/4)sin(π/6)

=0.5√2*0.5√3+0.5√2*0.5=(√6+√2)/4

【12】

cos(5π/12)=cos(π/4+π/6)

=cos(π/4)cos(π/6)-sin(π/4)sin(π/6+

=0.5√2*0.5√3-0.5√2*0.5=(√6-√2)/4

【2】

tan(5π/24)=[1-cos(5π/12)]/sin(5π/12)

=[1-(√3-1)/(2√2)]/[(√3+1)/(2√2)]

=(2√2)/(√3+1)-(√3-1)/(√3+1)

=(√6-√2)-(2-√3)

=(√6+√3)-(2+√2)

=(√2+1)(√3-√2)