Question

plz do question 3 will mark as brainliestplz do question 3 will mark as brainiest

Answer 1

Step-by-step explanation:

We have,

$\rm \: \frac{ \sin(A) + \cos(A) }{\sin(A) - \cos(A)} + \frac{\sin(A) - \cos(A)}{\sin(A) + \cos(A)}$

$\rm \: = \frac{ \{\sin(A) + \cos(A) \}^{2} + \{\sin(A) - \cos(A) \}^{2} }{ \{\sin(A) - \cos(A) \} \{ \sin(A) + \cos(A) \}}$

$\rm \: = \frac{ 2(\{\sin(A) \} ^{2} + \{ \cos(A) \}^{2} ) }{ \{\sin^{2} (A) - \cos^{2} (A) \}}$

$\rm \: = \frac{ 2(\sin ^{2} (A) + \cos^{2} (A)) }{ \{\sin^{2} (A) - \cos^{2} (A) \}}$

$\rm \: = \frac{ 2(1) }{ 1 - \cos^{2} (A) - \cos^{2} (A) }$

$\rm \: = \frac{ 2(1) }{ 1 - 2\cos^{2} (A) }$

$\rm \: = \frac{ 2 }{ 1 - 2\cos^{2} (A) }$