Question

Prove that:- Cos theta/1-sin theta = 1+sin theta/ cos theta​

Answer 1

To prove :

$\star \: \dfrac{ \cos \theta}{1 - \sin\theta} = \dfrac{1 + \sin \theta\: }{ \cos\theta}$

Take

LHS :

$\implies \: \dfrac{ \cos\theta}{1 - \sin\theta}$

Here ,

• Rationalise the denominator :

$\implies \: \dfrac{ \cos\theta}{1 - \sin\theta} \times \dfrac{1 + \sin\theta}{1 + \sin \theta} \\ \\ \implies \: \dfrac{ \cos\theta(1 + \sin\theta)}{ {1}^{2} - { \sin}^{2} \theta} \\ \\ \implies \: \dfrac{ \cos\theta(1 + \sin\theta)}{1 - { \sin}^{2} \theta } \\ \\ \implies \: \dfrac{ \cancel{\cos\theta}(1 + \sin\theta)}{ \cancel{{ \cos}^{2} \theta }} \\ \\ \implies \: \dfrac{1 + \sin \theta}{ \cos \theta}$

LHS = RHS .

$\huge \red{ \mathfrak{proved}}$

Formula used :

$\star \: \bold{ { \sin}^{2} \theta - { \cos}^{ 2 } \theta = 1} \\ \\ \star \bold{ (x - y)(x + y) = {x}^{2} - {y}^{2} }$

Answer 2

Answer:

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