About tension (is this correct ?)

[live4physics]

If I want to know the tension on strings is possible use the algebra below ?

$$\Sigma$$F_x = cos$$\theta$$ T₂-T₃ = 0
and
$$\Sigma$$F_y = sen$$\theta$$T₂-T₁ = 0
so
T₂=T₃/cos$$\theta$$
and
T₂ = T₁/sen$$\theta$$
so
T₁cos$$\theta$$ = T₃sen$$\theta$$

is this correct ?

Thanks

obs: this is not my home work, but a self study.

 

[Doc Al]

is this correct ?

Yes, looks good. (Use sinθ, not senθ.) You can go further by expressing T₁ in terms of the mass m.

obs: this is not my home work, but a self study.

Nonetheless, this sort of textbook-style problem belongs in the "HW" forum, even if it's self study.