Question

Two forces p and q are in the ratio p:q= 1:2. if their resultant is at an angle tan-1(√3/2) [tan inverse √3/2] to vector p, then angle between p and q is :

Answer 1

The formula for direction of the resultant force is given by $\alpha$ = $tan^{-1}$ Qsin θ / (P + Q cos θ).

In the data, it is given that P and Q are in the ratio 1:2. Also, it is mentioned that the angle is $tan^{-1}$ √3/2. 

By substituting these values into the formula, we get
$tan^{-1}$ √3/2 = $tan^{-1}$ 2sin θ / (1 + 2 cos θ)
√3/2 = 2sin θ / (1 + 2 cos θ)

Now you can go ahead and solve this equation to find the value of θ. But that will be a tedious process and demands some time. Therefore, if this is a competitive exam question, I suggest you to use the inspection method instead. This method involves substituting common values of θ for which the trigonometric ratios are already known.

For example, let us substitute θ=60°
Then, √3/2 = 2sin 60°  / (1 + 2 cos 60°)
√3/2 = (2 * √3/2) / (1 + 2 * 1/2)
√3/2 = (√3) / (1+1)
√3/2 = √3/2
LHS=RHS

Hence we conclude that the angle between P and Q is  60°

Answer 2

Answer:

The answer is 60°....please vote and share