Question

Show that :
$\sqrt{1 - \sin(a ) } \div \sqrt{1 + \sin(a ) } \: = \sec(a) - \tan(a)$

Answer 1

rationalise ur denominator by multiplying root of (1-sina), so you get a perfect square in numerator nd root of (1-sin^2a) which is cosa. so finally you get,

$\frac{1-sina}{cos a}$

give the numerator individual denominator, so u get,

$\frac{1}{cos a} - \frac{sin a}{cos a} =sec a- tan a$

hope this helps!