Question

Помогите решить.
cos (arccos (-sqrt (3)/2))+sin (arcsin (-1/2))

Answer 1

Ответ:

$\boxed{\ cos(arccosx)=x\ ,\ esli\ \ -1\leq x\leq 1\ \ ,\ \ sin(arcsinx)=x\ ,\ esli\ \ -1\leq x\leq 1\ }$

$cos\Big(arccos(-\dfrac{\sqrt3}{2})\, \Big)+sin\Big(arcsin(-\dfrac{1}{2})\, \Big)=\\\\=cos\Big(\pi -arccos\dfrac{\sqrt3}{2}\, \Big)+sin\Big(-arcsin\dfrac{1}{2}\, \Big)=\\\\=cos\Big(\pi -\dfrac{\pi }{6}\, \Big)-sin\Big(arcsin\dfrac{1}{2}\, \Big)=\\\\=cos\Big(\dfrac{5\pi }{6}\, \Big)-sin\Big(\dfrac{\pi}{6}\, \Big)=-\dfrac{1}{2}-\dfrac{1}{2}=-1$