Respuesta :

Answer:

[tex] \huge \boxed{ \boxed{2 + \sqrt{3}}} [/tex]

Explanation:

to understand this

you need to know about:

  • trigonometry
  • PEMDAS

given:

  • [tex] \frac{1 + \cos( {30}^{o} ) }{1 - \sin( {30}^{o} ) } [/tex]

tips and formulas:

  • cos(30°)=[tex]\frac{\sqrt{3}}{2}[/tex]
  • [tex] \sin( {30}^{o} ) = \frac{1}{2} [/tex]

let's solve:

  1. [tex] \sf sustitute \: the \: value \: of \: \sin( {30}^{o} ) and \cos( {30}^{o} ) \\ \sf \frac{1 + \frac{ \sqrt{3} }{2}}{1 - \frac{1}{2} } [/tex]
  2. [tex] \sf simplify : \\ \frac{ \frac{2 + \sqrt{3} }{2} }{ \frac{1}{2} } [/tex]
  3. [tex] \sf simplify(fraction) : \\ \frac{2 + \sqrt{3} }{2} \div \frac{1}{2} \\ \frac{2 + \sqrt{3} }{2} \times 2 \\ \therefore 2 + \sqrt{3} [/tex]

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