如何证明(tanb X sinb)/(tanb - sinb)与(tanb + sinb)/(tanb X sinb)相等
问题描述：
如何证明(tanb X sinb)/(tanb - sinb)与(tanb + sinb)/(tanb X sinb)相等
答
(tanb X sinb)/(tanb - sinb)
=(tanb X sinb)/(tanb - tanbcosb)
=sinb/(1-cosb)
=sinb(1+cosb)/（1-cosb）（1+cosb)
=(1+cosb)/sinb
(tanb + sinb)/(tanb X sinb)
=(tanb + tanbcosb)/(tanb X sinb)
=(1+cosb)/sinb
答
(tanb X sinb)/(tanb - sinb)=(tanb + sinb)/(tanb X sinb)
tan^2b*sin^2b=tan^2b-sin^2b
sin^4b=sin^2b-sin^2bcos^2b
=sin^2b(1-cos^2b)
=sin^4b
成立