Question

1+sin a by 1 - sin a - 1 - sin a by 1+ sin a = 4 sec a. tan a​

Answer 1

Step-by-step explanation:

$\frac{1 + \sin(a) }{1 - \sin(a) } - \frac{1 - \sin(a) }{1 + \sin(a) }$

$= \frac{ {(1 + \sin(a)) }^{2} - {(1 - \sin(a)) }^{2} }{(1 - \sin(a)) \times(1 + \sin(a)) }$

$\frac{1 + \sin^{2}a + 2 \sin( a) - 1 - \sin ^{2}a + 2 \sin(a) }{1 - \sin ^{2}a }$

$\frac{4 \sin(a) }{ { \cos }^{2} a} = 4 \times \frac{ \sin(a) }{ \cos(a) } \times \frac{1}{ \cos(a) }$

$= 4 \sec(a) \tan(a)$