Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

Given : $f(\cos 4\theta )=\frac{2}{2-{\sec }^2\theta }=\frac{2{\cos }^2\theta }{2{\cos }^2\theta -1}$ $=\frac{1+\cos 2\theta }{\cos 2\theta }=1+\frac{1}{\cos 2\theta }$ Let $\cos 4\theta =\frac{1}{3}\Rightarrow 2{\cos }^{2}2\theta -1=\frac{1}{3}\Rightarrow \cos 2\theta =\pm \sqrt{\frac{2}{3}}$ $\therefore f(\cos 4\theta )=1+\frac{1}{\cos 2\theta }=1\pm \sqrt{\frac{3}{2}}$ or $f\left(\frac{1}{3}\right)=1\pm \sqrt{\frac{3}{2}}$