Question

# mods challenge

need a verified ✔️answer

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Answer 1

Answer:

LHS = √(1 + sin∅)/√(1 - sin∅)

= √(1 + sin∅) × √(1 + sin∅)/√(1 -sin∅)×√(1 +sin∅)

= √(1 + sin∅)²/√(1 -sin²∅)

= (1 + sin∅)/√cos²∅

= (1 + sin∅)/cos∅

= 1/cos∅ + sin∅/cos∅

= sec∅ + tan∅ = RHS

Answer 2

$\large\red{\underline{{\boxed{\textbf{to \: prove: }}}}} \\ \\ \huge : \implies \: \huge \: \sqrt{ \frac{1 + \sin \: A }{1 - \ \sin \: A} } = \sec \: A\: + \: \tan \: A</p><p></p><p>$

$\large\red{\underline{{\boxed{\textbf{solution: }}}}} \: \\ \\ LHS = \huge \: \sqrt{ \frac{1 + \sin \: A}{1 - \sin \: A} } \\ \\ = \: \sqrt{ \frac{(1 + \sin \: A)(1 + \sin \: A) }{(1 - \sin \: A)(1 + \sin \: A) } } \\ \\ = \sqrt{ \frac{(1 + \sin \: A) ^{2} }{1 - \sin ^{2} } } \\ \\ = \frac{(1 + \sin \: A)}{ \sqrt{ \cos^{2} \: A } } \\ \\ = \frac{1 + \sin \: A }{ \cos \: A} \\ \\ = \frac{1}{ \cos \: A } \: + \: \frac{ \sin \: A}{ \cos \: A} \\ \\ = \sec \: A\: + \: \tan \: A \: = RHS \\ \\ </p><p>$

LHS = RHS

HENCE VERIFIED ✔