Two people pull upwards to the left and upwards to the right with two large forces in order to lift a 1kg book by two cables. if each cable make 1- degree angle with the horizontal, then what is the tension in the cables?

The weight of the book is (mass) x (gravity) = (1kg) x (9.8m/s²) = 9.8 newtons
                                                                                            (about 2.2 pounds)
The upward force on the book is the sum of the
upward force from each cable (each person).

The forces from the two people must be equal, otherwise the book
would move sideways one way or the other.

Now for the big cookie:  If the cables are within 1 degree of
being horizontal, then how much of each person's force winds
up being vertical to lift the book ?

If a force 'F' is directed 1 degree above horizontal, then
its strength in the horizontal direction is   F x cos(1), and
its strength in the vertical direction is   F x sin(1).

Each person is pulling with a force  F.
His vertical component is  F x sin(1).
Two of these hold the 1-kg book up.

                             2F sin(1) = 9.8 newtons

Divide each side by 2 :      F sin(1) = 4.9 newtons

Divide each side by  sin(1)    F = 4.9 / sin(1) = 280.7 newtons (rounded)
                                                                    (about 63 pounds)

This is the tension in each cable.               


That's why, technically, it's impossible to make the cable or string
perfectly horizontal, even when there's nothing hanging from it. 
When the force is perfectly horizontal, its vertical component is
zero, so it would take an infinite force to hold anything horizontal,
even the weight of the string itself. 
From another viewpoint ... If the string or cable is almost horizontal,
then the tension in it is already so great that you can break it with
just a light push in the center with your finger.