tan75=sin75/cos75=√6-√2/√6+√2=2+√3

题目

tan75=sin75/cos75=√6-√2/√6+√2=2+√3
√6-√2/√6+√2=2+√3怎么得到?

答案

题目有误.应该是:
tan75=sin75/cos75=(√6+√2)/(√6-√2)=2+√3
tan75=sin75/cos75
=(sin45*cos30+cos45sin30)/(cos45cos30-sin45*sin30)
={[(√2)/2]*[(√3)/2]+[(√2)/2]*(1/2)}/{[(√2)/2]*[(√3)/2]-[(√2)/2]*(1/2)}
={[(√6)/4]+[(√2)/4]}/{[(√6)/4]-[(√2)/4]}
=[(√6+√2)/4]/[(√6-√2)/4]
=(√6+√2)/(√6-√2)
=(√6+√2)^2/[(√6-√2)(√6+√2)]
=(6+2√12+2)/(6-2)
=(8+4√3)/4
=2+√3