求证：2sin(a)-sin2(a)/2sin(a)+sin2(a)=tan^2(a/2)顺便告诉小弟此类题型解题思路,在下感激不尽~
问题描述：
求证：2sin(a)-sin2(a)/2sin(a)+sin2(a)=tan^2(a/2)
顺便告诉小弟此类题型解题思路,在下感激不尽~
答
(2sina-sin2a)/(2sina+sin2a)
=(2sina-2sinacosa)/(2sina+2sinacosa)
=(1-cosa)/(1+cosa)
=[(cos^2 a/2 +sin^2 a/2)-(cos^2 a/2 -sin^2 a/2)]/[(cos^2 a/2 +sin^2 a/2)+(cos^2 a/2 -sin^2 a/2)]
=(2sin^2 a/2)/(2cos^2 a/2)
=tan^2 a/2