Dear Rohan

One thing should be noted here that length of the rope is constant.

let the length between the wedge and lower pully is x2

and    length between the block and upper pully is x1

           +dx₁/dt =v₁

and      -dx₂/dt =v₂

Now length of the rope is constant

   so   x2+ (x₂²+l²)^1/2 +x1 =coonstant    where l is a vertical distance between two pully which is constant

now differentiate and put +dx₁/dt =v₁ 

and      -dx₂/dt =v₂

and  sinθ =x2/(x₂²+l²)^1/2

and rearrange you will get

v1=v2(1+sinθ)

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