If \(\frac{cos ∝}{sin β}\) = n and \(\frac{cos ∝}{cos β}\) = m ; then the value of cos² β is?

\(\frac{1}{m^2 + n^2}\)

Put ∝ = 60° ; β = 30°

\(\frac{cos ∝}{sin β}\) = \(\frac{\frac{1}{2}}{\frac{1}{2}}\) = 1 = n ; 

\(\frac{cos ∝}{cos β}\) = \(\frac{\frac{1}{2}}{\frac{\sqrt {3}}{2}}\) = \(\frac{1}{\sqrt {3 }}\) = m

checking value from options ;

⇒ cos² β = cos²30° =  \(\frac{3}{4}\) = \(\frac{1}{\frac{1}{3} + 1}\) = \(\frac{1}{m^2 + n^2}\)        {beacause m = \(\frac{1}{\sqrt {3 }}\), so m² = \(\frac{1}{3}\)