Question

plz answer faster
20 points​

Answer 1

SOLUTION

Given,

$(sin \theta + sec \theta) {}^{2} + (cos \theta + cosec \theta) {}^{2} \\ = > (sin \theta + \frac{1}{cos \theta} ) {}^{2} + (cos \theta + \frac{1}{sin \theta} ) {}^{2} \\ \\ = > {sin}^{2} \theta + \frac{1}{ {cos}^{2} \theta } + \frac{2sin \theta}{cos \theta} + {cos}^{2} \theta + \frac{1}{ {sin}^{2} \theta } + \frac{2cos \theta}{sin \theta} \\ \\ = > ( {sin}^{2} \theta + {cos}^{2} \theta) + ( \frac{1}{ {cos}^{2} \theta} + \frac{1}{ {sin}^{2} \theta } ) + 2( \frac{sin \theta}{cos \theta} + \frac{co s \theta}{si n \theta} ) \\ \\ = > 1 + ( \frac{ {sin}^{2} \theta + {cos}^{2} \theta }{ {sin}^{2} \theta. {cos}^{2} \theta } ) + 2( \frac{ {sin}^{2} \theta + {cos}^{2} \theta }{sin \theta.cos \theta} ) \\ \\ = > 1 + \frac{1}{ {sin}^{2} \theta. {cos}^{2} \theta } + 2( \frac{1}{sin \theta.cos \theta} ) \\ \\ = > (1 + \frac{1}{sin \theta.cos \theta} ) {}^{2} \\ \\ = > (1 + sec \theta.cosec \theta) {}^{2} \: \: \: \: \: </u><u>[</u><u>Pr</u><u>oved</u><u>]</u><u>$

hope it helps ☺️