Question

1. Daca x∈(0;$\frac{ \pi }{2}$) si cos2x=$\frac{1}{2}$, calculati sinx.
2.calculati: cos²10⁰+cos²50⁰+cos²70⁰=$\frac{3}{2}$

Answer 1

x,y $x,y.apartinand.(0.pi/2)-\ \textgreater \ x,y.apartin.Cadranului.1.$
$sin.x\ \textgreater \ 0 ,si.cosx\ \textgreater \ 0;sin.y\ \textgreater \ 0,si.cos.y\ \textgreater \ 0$

$cos(x-y)=cosx·cosy+sinx·siny$
Se foloseste formula de calcul a functiilor trigonometrice a sumei si a diferentei intre unghiuri
sin²x+cos²x=1 
sin²x=1-(1/7)²
sin²x=1-1/49
sinx=√48/49
sinx=4√3/7
sin²y+cos²y=1
sin²y=1-(13/14)²
sin²y=1-169/196
siny=√27/196
siny=3√3/13
cos(x-y)=1/7·13/14+4√3/7·3√3/14=13/98+36/98
cos(x-y)=49/98
cos(x-y)=1/2