Question

Prove that:
(1 - sin x)/(1 + sin x) = ( sec x - tan x)²


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Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

PROVE THAT

$\frac{(1 - \sin(x)) }{(1 + \sin(x)) } = ( \sec(x) - \tan(x) ) ^{2}$

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$= ( \sec(x) - \tan(x) ) ^{2}$

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

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

$= \frac{(1 - \sin(x)) ^{2} }{1 - \sin(x) }$

$= \frac{(1 - \sin(x))(1 - \sin(x)) }{(1 + \sin(x))(1 - \sin(x) )}$

$= \frac{1 - \sin(x) }{1 + \sin(x) }$

RHS =LHS

HENCE PROVED