Question

Rezolvati si explicati va rog cum se rezolva exercitiul 6 din imagine

Answer 1

(sin π/7-cos a)²+(cos π/7- sin a)²=2<=>sin²π/7+cos²a-2sin π/7*cos a+cos²π/7+sin²a-2sin a*cos π/7=2

sin²π/7+cos²π/7=1

sin²a+cos²a=1

1+1-2(sin π/7*cos a+sin a*cos π/7)=2<=>(sin π/7+cos π/7)(cos a+sin a)=0=> cos a+sin a=0

cos a+sin a=0 |:cos a=>1+tg a=0=>tg a=-1=> a={arctg(-1)+kπ,k∈Z}={-π/4+kπ,k∈Z}