Question

Sa se verficice egalitatea:
arctgX+arcctgX=X/2

Answer 1

Ecuatia corecta este: arctgx+arcctgx=$\frac{ \pi }{2}$, o sriem sub forma :
arctgx=$\frac{ \pi }{2}$-arcctgx, aplicam in ambi membri tangenta si tinem cont de formula tg($(\frac{ \pi }{2}-x)=ctgx$, si de proprietatile functiilor inverse: tg(arctgx)=x si ctg(arcctgx)=x, si obtinem : tg(arctgx)=tg($\frac{ \pi }{2}-arcctgx)$, deci x=ctg(arcctgx) adica x=x, egalitatea este verificata.