题目

在三角形abc中,abc为三角形三角,(sin a-sin b)(sin a+sin b)怎么得到sin (a+b)sin (a-b)?另外(30sin 30度)/sin 15度怎么得到60cos

提问时间：2020-11-03

答案

(sin a-sin b)(sin a+sin b)
=(sin a)^2-(sin b)^2
=(sin a)^2-(sin a)^2(sin b)^2-(sin b)^2+(sin a)^2(sin b)^2
=(sin a)^2[1-(sin b)^2]-(sin b)^2[1-(sin a)^2]
=(sin a)^2(cos b)^2-(sin b)^2(cos a)^2
=(sinacosb+sinbcosa)(sinacosb-sinbcosa)
=sin (a+b)sin (a-b)
(30sin 30度)/sin 15度
=(30sin 2*15度)/sin 15度
=(30*2*sin 15度cos15度)/sin 15度
=60cos 15度