Question

√1+cos x/√1-cos x = cosec x + cot x

Answer 1

plese tell me helpful or not and you can follow me

Answer 2

Answer:

$\frac{ \sqrt{1 + \cos \: x } }{ \sqrt{ 1 - \cos \: x } } = \cosec \: x \: + \cot \: x$

Step-by-step explanation:

solution------>

Given :-

$\frac{ \sqrt{1 + \cos \: x } }{ \sqrt{ 1 - \cos \: x } } = \cosec \: x \: + \cot \: x$

LHS =

$\frac{ \sqrt{1 + \cos \: x } }{ \sqrt{ 1 - \cos \: x } } \: \\ \\ multiply \: with \: the \: \sqrt{1 + \cos \: x } \\ \\ we \: get \\ \frac{ \sqrt{1 + \cos \: x } }{ \sqrt{ 1 - \cos \: x } } \: \times \sqrt{ \frac{1 + \cos \: x }{1 - \cos \: x } } \\ \\ we \: get \\ \\ \frac{ \sqrt{ {(1 + cosx)}^{2} } }{ \sqrt{1 - {cos \: x}^{2} } } \\ \\ \sqrt{ \frac{ ({1 + \cos \: x })^{2} }{ {\sin \: x}^{2} } } .........1 - { \ \cos \: x }^{2} = { \sin \: x }^{2} \\ \\ \\ taking \: squre \: root \: out \: we \: get \\ \\ \frac{1 + \cos \: x }{ \sin \: x } \\ \\ now \: split \: this \\ \\ \frac{1}{ \sin \: x } + \frac{ \cos \: x }{ \sin \: x } \\ \\ we \: get \\ \\ cosec \: x + cot \: x.................( \frac{1}{sin \: x} = cosec \: x \: and \: \frac{cos \: x}{sin \: x} = cot \: x \\ \\ there \: for \: its \: prove$

$\frac{ \sqrt{1 + \cos \: x } }{ \sqrt{ 1 - \cos \: x } } = \cosec \: x \: + \cot \: x$