Prove That, $sec\left(\frac{\pi }{4} + \theta \right)\sec \left(\frac{\pi }{4} – \theta \right)$ = $2sec2\theta$
L.H.S: $sec\left(\frac{\pi }{4} + \theta \right)\sec \left(\frac{\pi }{4} – \theta \right)$
= $\frac{1}{\cos \left(\frac{\pi }{4} + \theta \right)cos\left(\frac{\pi }{4} – \theta \right)}$
= $\frac{2}{2\cos \left(\frac{\pi }{4} + \theta \right)cos\left(\frac{\pi }{4} – \theta \right)}$
= $\frac{2}{\cos \left(\frac{\pi }{4} + \theta + \frac{\pi }{4} – \theta \right) + cos\left(\frac{\pi }{4} + \theta – \frac{\pi }{4} + \theta \right)}$
= $\frac{2}{\cos \frac{\pi }{2} + cos2\theta }$
= $\frac{2}{\cos 2\theta }$
= $2sec2\theta$
=R.H.S [Proved]