Question

Plz ans this que plz ​

Answer 1

$\tt {(tan\theta + \frac{1}{cos\theta})}^{2} + {(tan\theta - \frac{1}{cos\theta})}^{2} \\ \\ \tt \longrightarrow {tan}^{2}\theta + 2\frac{tan\theta}{cos\theta} + \frac{1}{{cos}^{2}\theta} + {tan}^{2}\theta - 2\frac{tan\theta}{cos\theta} + \frac{1}{{cos}^{2}\theta} \\ \\ \tt \longrightarrow 2{tan}^{2}\theta + \frac{2}{{cos}^{2}\theta} \\ \\ \tt •\longrightarrow 2{sin}^{2}\theta{{cos}^{2}\theta} + \frac{2}{{cos}^{2}\theta} \\ \\ \tt \longrightarrow \frac {2{sin}^{2}\theta + 2 }{1-{sin}^{2}\theta} \\ \\ \tt \longrightarrow 2\frac{1+{sin}^{2}\theta}{1-{sin}^{2}\theta} \\ \\ \tt \longrightarrow R.H.S \\ \\ \tt \red{Hence\:proved}$