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Fie x aparține R astfel încât sin x + cos x =5/4

Răspuns :

deoarece tgπ/4=1  poti  scrie
sinx+tgπ/4cosx=5/4
sinx+(sinπ/4/cosπ/4)*cosx=5/4
cosπ/4*sinx+sinπ/4*cosx=5/4
sin(x+π/4)=5/4*cosπ/4
sin(x+π/4)=5/4*√2/2
x+π/4=arcsin[5/4*√2/2]
x=arcsin(5/4*√2/2)-π/4
solutia   generala
x=(-1)^k*[arcsin5/4*√2/2-π/4]+kπ