Question

Answer this question

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Answer 1

Step-by-step explanation:

★Given -

• $\rm{ \sqrt{ \dfrac{1 + \sin \theta}{1 - \sin \theta } } }$

★To prove -

• $\rm{ { \dfrac{1 + \sin \theta }{cos\theta} } }$

★Concept -

• Here, we'll use the concept of rationalising the denominator to get the required answer. Let's do it!!

★Solution -

LHS

$\longmapsto \rm{ \sqrt{ \dfrac{1 + \sin \theta }{1 - \sin\theta } } }$

$\longmapsto \rm{ \sqrt{ \dfrac{1 + \sin\theta }{1 - \sin \theta } \times \dfrac{1 + \sin \theta }{1 + \sin\theta} }}$

$\longmapsto \rm{ \sqrt{ \dfrac{(1 + \sin\theta)^{2} }{ {1}^{2} - \sin ^{2} \theta} }}$

$\longmapsto \rm{ \sqrt{ \dfrac{(1 + \sin\theta)^{2} }{ \cos ^{2} \theta} }}$

Since, sin²∅ + cos²∅ = 1

=> cos²∅ = 1 - sin²∅

$\longmapsto \rm{\orange{{ \dfrac{1 + \sin\theta }{ \cos \theta}=LHS }}}$