Question

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)si

Answer 1

(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