In Hc.Verma concepts of phy vol-1 pg.72 ...in the worked out examples problem no.1 how did they take the horizontal components and the vertical components .???Can u explain this to me ???I will b happy to approve plzzz..helpppp meee..Aieee approaching givin me the nightmares pleaase helppppAlways gonna be approved !!!Thanks !@!

for this we have to consider a horizontal & vertical axis or x & y axis ...

tension can have 2 components , Tcos@ & Tsin@  ....

for left string tension has 2 components T₂cosB along horizontal & T₂sinB along verticle upward ...

for ryt string components are T₁cos@ along horizontal & T₁sin@ along verticle upward ...

now , at this stage we have to balance all the forces since we know that body is in equilibrium so no net force

exists in any direction ...

for upward direction , net force = T₁sin@ + T₂sinB

for downward dirctn , net force is weight of body = mg

for verticle equilibrium net force along verticle direction is 0 ..

Tsin@ + TsinB = mg          .......................1

for horizontal direction , T₁cos@ = T₂sinB        ...........2      (net force 0)

now solve 1 & 2 get the desired result

one more method can be used for all systems which are in equilibrium ,

lami's theorem =>

 the Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear forces, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding forces. According to the theorem,

where A, B and C are the magnitudes of three coplanar, concurrent and non-collinear forces, which keeps the object in static equilibrium, and

α, β and γ are the angles directly opposite to the forces A, B and C respectively.

Lami's theorem is applied in static analysis of mechanical and structural systems.