求证:2sinα+sin2α=2sin^3α/(1-cosα)

题目

求证:2sinα+sin2α=2sin^3α/(1-cosα)

答案

2sina+sin2a
=2sina+2sinacosa
=2sina(1+cosa)=2sin^3a(1+cosa)/sin^2a
=2sin^3a(1+cosa)/(1-cos^2a)
=2sin^3a/(1-cosa)