If \(\frac{cos ∝}{sin β}\) = n and \(\frac{cos ∝}{cos β}\) = m ; then the value of cos2 β is? |
\(\frac{1}{m^2 + n^2}\) \(\frac{n^2}{m^2 + n^2}\) \(\frac{m^2}{m^2 + n^2}\) m2 - n2 |
\(\frac{1}{m^2 + n^2}\) |
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 = \(\frac{1}{3}\) |