This picture was obtained from a journal in which this equation was written:
$$F_x l \cos\theta = F_y l \sin\theta $$
The explanations stated that this was because the torque of pivot with respect to the bob is zero, this is my approach:
$$\vec l= -l\sin\theta \hat i -l\cos\theta \hat j $$ $$\vec F= F_x \hat i + F_y \hat j$$ $$\vec \tau=\vec l \times \vec F = -F_y l\sin\theta \hat k + F_x l\cos\theta \hat k$$
so assuming $\vec\tau =0$ :
$$F_y l \sin\theta \hat k=F_x l\cos\theta \hat k$$
$$F_y l \sin\theta = F_x l \cos \theta$$
My question is Why can we say $\vec\tau = 0$ ?