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rezolvati in multimea(0,π/2) ecuatia 2cosx-√3=0




Răspuns :

in x ∈( 0 , π/2 ) 
cosx =√3/2 
daca x= π/6
[tex]cosx= \frac{ \sqrt{3} }{2} [/tex]
x=[tex]arccos \frac{ \sqrt{3} }{2}+2k \pi , \pi dinZ [/tex]    sau x=-[tex]arccos \frac{ \sqrt{3} }{2}+2n \pi [/tex]
x=π/6+2kπ sau x=-π/6+2nπ
selectam solutiile
0≤π/6+2kπ≤π/2      sau 0≤-π/6+2nπ≤π/2
-π/6≤2kπ≤π/2-π/6   sau π/6≤2nπ≤π/2+π/6
-1/12≤k≤1/6             sau 1/12≤n≤1/3
   k=0                             n∉Z
deci x=π/6