The resultant force(R) of two forces (P and Q) acting on a single point, with an angle θ between them, will be equal to

Explanation:

Law of Parallelogram of Forces:

• According to this Law "If two coplanar forces, acting simultaneously on a point of the body, be represented in magnitude and direction by the two adjacent sides of a parallelogram then their results can be represented in magnitude and direction parallelogram." by the diagonal of the parallelogram".
• This method is only useful for finding the resultant of only two coplanar concurrent forces.

OA =P  &  OB = Q 
Now from the figure (Corresponding angles)
∠AOB = ∠DAC = α
Now in △ADC 
As we know 
Sinα = perpendicular/hypotenuse
Cosα  = base / hypotenuse
So,
sinα = CD/AC 
CD = AC sinα  
And
cosα = AD/AC
AD = AC cosα
Now in △ODC,

OC² = OD² + CD² = (OA + AD)² + CD² 
(since OD = OA + AD, from figure)
= OA² + AD² + 2 OA × AD + CD²
= OA² + (AC cosα )² + 2 OA × AC cosα + (AC sinα)²
= OA² + AC² cos²α + 2OA × AC cosα + (AC² sin²α)
= OA² + AC² (sin²α + cos²α ) + 2 OA × AC(cos α) 
As we know,
sin²α + cos²α = 1
Then
OC² = OA² + AC ²(1) + 2 OA × AC (cos α) 
OC² = OA² + AC ² + 2 OA × AC (cos α) 
Since, OA = P, AC = AB = Q, OC = R
So,
R²= P ² + Q ² + 2P × Q cosα
Then,
Resultant, R = \(\sqrt{P^2 + Q^2 + 2PQ cos\alpha}\)