Question

(sin75度+cos75度)/(sin75度-cos75度)=?

Answer 1

sin75+cos75
=sin75+sin15
=2sin(75+15)/2cos(75-15)/2
=2sin45cos30
=√6/2

sin75-cos75
=sin75-sin15
=2cos(75+15)/2sin(75-15)/2
=2cos45sin30
=√2/2
(sin75度+cos75度)/(sin75度-cos75度)
=√6/2 / √2/2
=√3

Answer 2

sin75=sin(45+30)=sin45cos30+cos45sin30=(√2+√6)/4
cos75=cos(45+30)=cos45cos45-sin45sin30=(√6-√2)/4
∴(sin75度+cos75度)/(sin75度-cos75度)
=[(√2+√6)/4+(√6-√2)/4]/[(√2+√6)/4-(√6-√2)/4]
=√3