Question

cos A. cot A / 1-sin A = 1 + cosec A​

Answer 1

$\huge \red{solution}$

$\cos(a) \frac{ \cot(a) }{1 - \sin(a) } = 1 + \csc(a)$

LHS

$\frac{ \cos(a) \frac{ \cos(a) }{ \sin(a) } }{1 - \sin(a) } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \therefore \cot(a) = \frac{ \cos(a) }{ \sin( a) }$

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

$\frac{1 - { \sin }^{2} a}{ \sin(a) (1 - \sin(a)) } \: \: \: \: \: \: \: \: \: \: \: \: \therefore \: { \cos }^{2} a = 1 - { \sin }^{2} a$

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

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

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

$\csc \: a \: + 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \therefore \frac{1}{ \sin \: a } = \csc \: a$

$\red{rhs = \cos \: a + 1}$

$\green{hopu \: u \: like \: my \: answer}$

$\green{thank \: u \: and \: have \: a \: nyc \: day}$