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aflati x:

arctg x+arcctg 1/3=pi/2


Răspuns :

fie arctgx=a⇔x=tga
si arcctg1/3=b⇔1/3=ctgb
Atunci: a+b=π/2
si cos(a+b)=cosπ/2=0⇔cosa·cosb-sina·sinb=0 I  :sina·sinb⇔
⇔ctga·ctgb=1⇔1/tga·1/3=1⇔tga=1/3⇔x=1/3