Question

Daca x∈(0, pi/2) si cosx = √2/2 aratati ca tg x= 1

Answer 1

sin²x+cos²x=1
sin²x+(√2/2)²=1=>
sinx=√(1-2/4)=√2/2
tgx=sinx/cosx=(√2/2)/(√2/2)=1

Answer 2

sin x=+-√(1-cos²x)=+-√(1-1/2)=+-√1/2=+-1/√2
cum x∈(0;π/2)⇒sinx=1/ √2

atunci tgx=sinx/cosx= (1/√2)/(√2/2)=(√2/2)/(√2/2)=1


ALTFEL
cos x=√2/2
x= 2kπ+-arccos(√2/2)=2kπ+-π/4
cum x∈(0;π/2)⇒x=π/4
 atunci
tgx=tgπ/4=1
as simple as that!