Giải Khám phá 3 trang 22 Toán 11 tập 1 Chân trời

a) $cos(\alpha -\beta )+cos(\alpha +\beta )$

= $cos(\alpha ).cos(\beta ) + sin(\alpha ).sin(\beta ) + cos(\alpha ).cos(\beta ) - sin(\alpha ).sin(\beta )$

= $2.cos(\alpha ).cos(\beta )$

$cos(\alpha -\beta )-cos(\alpha +\beta )$

= $cos(\alpha ).cos(\beta ) + sin(\alpha ).sin(\beta ) - cos(\alpha ).cos(\beta ) + sin(\alpha ).sin(\beta )$

= $2.sin(\alpha ).sin(\beta )$

b) $sin(\alpha -\beta )+sin(\alpha +\beta ) $

= $sin(\alpha ).cos(\beta ) - cos(\alpha ).sin(\beta ) + sin(\alpha ).cos(\beta ) + cos(\alpha ).sin(\beta )$

= $2.sin(\alpha ).cos(\beta )$

$sin(\alpha -\beta )-sin(\alpha +\beta )$

= $sin(\alpha ).cos(\beta ) - cos(\alpha ).sin(\beta ) - sin(\alpha ).cos(\beta ) - cos(\alpha ).sin(\beta )$

= $-2.cos(\alpha ).sin(\beta )$