The greatest & the least magnitude of the resultant of two forces of constant magnitudes are P & Q respectively. If the forces act at an angle `2 alpha`, then prove that the magnitude of their resultant is given by `sqrt(P^(2) cos^(2) alpha+Q^(2) sin^(2) alpha)`.

Explanation

To prove that the magnitude of the resultant of two forces \( P \) and \( Q \) acting at an angle \( 2\alpha \) is given by

\[ R = \sqrt{P^2 \cos^2 \alpha + Q^2 \sin^2 \alpha}, \]

we can follow these steps:

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