Question

sec(pi/5)^2 - tan(pi/5)^2

Answer 1

$$\sec^ {2} \left(\frac {\pi}{5}\right) - \tan^ {2} \left(\frac {\pi}{5}\right) = \frac {1}{\cos^ {2} \left(\frac {\pi}{5}\right)} - \frac {\sin^ {2} \left(\frac {\pi}{5}\right)}{\cos^ {2} \left(\frac {\pi}{5}\right)} = \frac {\cos^ {2} \left(\frac {\pi}{5}\right)}{\cos^ {2} \left(\frac {\pi}{5}\right)} = 1$$

Answer: $\sec^2\left(\frac{\pi}{5}\right) - \tan^2\left(\frac{\pi}{5}\right) = 1$