Question

Rezolvati in R ecuatia:
cos x * ctg x - ctg x - sin x = 0

*Cum se afla DVA-ul ?
*cos^2 x - cos x - sin^2 x=0 ce fac mai departe ?

Answer 1

$cosx* \frac{cosx}{sinx}- \frac{cosx}{sinx} -sinx=0$
DVA:sinx∈[-1;1]
$cos^{2}x -cosx-sin^2x=0,x \neq n \pi [/text] [tex]cos^2x-cosx-1+cos^2x=0$
$2cos^2x-cosx-1=0$
fie cosx=m,m∈[-1;1]
[tex]2m^2-m-1=0 [/tex]
Δ=9
m=-1/2 ;m=1
revenim la substitutie
cosx=-1/2
cosx=1∉DVA
deci x=$\frac{2 \pi }{3}$
       x=-$\frac{2 \pi }{3}$