As the car is accelerating thus the string will not hang straight, it will make some angle . let the angle b/w original position and the displaced position as θ.

now resolve the tension,T when it make angle θ into sin & cos component.

on balancing u vyl get

Tcosθ = mg ( vertical component)

Tsinθ = ma ( horizontly)

now on squaring & adding these 2 eqn u vyl get

T²(sin²θ + cos²θ) = m²(g²+a²) => T= m√(g.²+a²)       here sin²θ+ cos²θ=1 is used