Question

Calculati sin(a+b+c)​

Answer 1

Formule generale folosite:

sin(x+y)=sin x·cos y + sin y·cos x

cos(x+y)=cos x·cos y-sin x·sin y

sin(a+b+c)=sin((a+b)+c)=

=sin(a+b)·cos c + sin c ·cos(a+b)=

=(sin a·cos b+sin b·cos a)·cos c+

sin c·(cos a·cos b- sin b·sin a)=

=sin a·cos b·cos c + cos a·sin b·cos c+ cos a·cos b·sin c -sin a·sin b·sin c=

(tg a=sin a/cos a => sin a=cos a·tg a)

=(cos a·tg a)·cos b·cos c + cos a·(cos b·tg b)·cos c +cos a·cos b·(cos c·tg c) -(cos a·tg a)·(cos b·tg b)·(cos c·tg c)=

=cos a·cos b·cos c · tg a + cos a·cos b·cos c · tg b + cos a·cos b·cos c · tg c -cos a·cos b·cos c · tg a · tg b · tg c=

= cos a·cos b·cos c·(tg a+tg b +tg c - tg a·tg b· tg c)

Raspuns:

sin(a+b+c)​=cos a·cos b·cos c·(tg a+tg b +tg c - tg a·tg b· tg c)