Question

Calcule a Expressão da imagem a seguir, sabendo que x = pi/3

Answer 1

Resposta:

${ \color{violet}{\bf{\boxed{ - \frac{ \sqrt{3} }{2} }}}}$

Explicação passo-a-passo:

OI, TUDO JÓIA? ツ

${ \color{violet}{\bf{ \frac{ \cos( \frac{\pi}{3} ) - \sec( \frac{\pi}{3}) - \tan( \frac{\pi}{3} ) }{ \tan( \frac{\pi}{3} ) + \sec( \frac{\pi}{3} ) } }}}$

${ \color{violet}{\bf{ \frac{ \frac{1}{2} - 2 - \sqrt{3} }{ \sqrt{3} + 2 } }}}$

${ \color{violet}{\bf{ \frac{ - \frac{3}{2} - \sqrt{3} }{ \sqrt{3} + 2} }}}$

Vamos pegar o numerador:

${ \color{violet}{\bf{ - \frac{3}{2} - \sqrt{3} }}}$

${ \color{violet}{\bf{ - ( \frac{3}{2} + \sqrt{3} )}}}$

${ \color{violet}{\bf{ - ( \frac{3}{2} + \frac{ \sqrt{3} }{1} ) }}}$

${ \color{violet}{\bf{ - ( \frac{3}{2} + \frac{2 \sqrt{3} }{2 \times 1} ) }}}$

${ \color{violet}{\bf{ - ( \frac{3}{2} + \frac{2 \sqrt{3} }{2} ) }}}$

${ \color{violet}{\bf{ - \frac{3 + 2 \sqrt{3} }{2} }}}$

Vamos juntar a fração novamente:

${ \color{violet}{\bf{ \frac{ - \frac{3 + 2 \sqrt{3} }{2} }{ \sqrt{3} + 2} }}}$

${ \color{violet}{\bf{ - \frac{ \frac{3 + 2 \sqrt{3} }{2} }{ \sqrt{3} + 2} }}}$

${ \color{violet}{\bf{ \frac{3 + 2 \sqrt{3} }{2} \div ( \sqrt{3} + 2) }}}$

${ \color{violet}{\bf{ \frac{3 + 2 \sqrt{3} }{2} \times \frac{1}{ \sqrt{3} + 2} }}}$

${ \color{violet}{\bf{ \frac{(3 + 2 \sqrt{3} ) \times 1}{2( \sqrt{3} + 2) } }}}$

${ \color{violet}{\bf{ \frac{3 + 2 \sqrt{3} }{2( \sqrt{3} + 2)} }}}$

Vamos pegar o sinal de novo:

${ \color{violet}{\bf{ - \frac{3 + 2 \sqrt{3} }{2( \sqrt{3} + 2)} }}}$

${ \color{violet}{\bf{ \frac{3 + 2 \sqrt{3} }{2( \sqrt{3} + 2)} \times \frac{ \sqrt{3} - 2}{ \sqrt{3} - 2 } }}}$

${ \color{violet}{\bf{ \frac{(3 + 2 \sqrt{3} ) \times ( \sqrt{3} - 2) }{2( \sqrt{3} + 2) \times ( \sqrt{3} - 2)} }}}$

${ \color{violet}{\bf{ \frac{(3 + 2 \sqrt{3} ) \times ( \sqrt{3} - 2) }{2(3 - 4)} }}}$

${ \color{violet}{\bf{ \frac{(3 + 2 \sqrt{3} ) \times ( \sqrt{3} - 2) }{2( - 1)} }}}$

${ \color{violet}{\bf{ \frac{(3 + 2 \sqrt{3} ) \times ( \sqrt{3} - 2)}{ - 2} }}}$

Vamos pegar o sinal de novo:

${ \color{violet}{\bf{ - \frac{(3 + 2 \sqrt{3} ) \times ( \sqrt{3} - 2)}{ - 2} }}}$

Separe o numerador:

${ \color{violet}{\bf{(3 + 2 \sqrt{3} ) \times ( \sqrt{3} - 2) }}}$

${ \color{violet}{\bf{3 \sqrt{3} - 3 \times 2 + 2 \sqrt{3} \sqrt{3} - 2 \sqrt{3} \times 2 }}}$

${ \color{violet}{\bf{3 \sqrt{3} - 6 + 2 \sqrt{3} \sqrt{3} - 2 \sqrt{3} \times 2}}}$

${ \color{violet}{\bf{3 \sqrt{3} - 6 + 6 - 2 \sqrt{3} \times 2 }}}$

${ \color{violet}{\bf{3 \sqrt{3} - 6 + 6 - 4 \sqrt{3} }}}$

Agora junte a fração de novo:

${ \color{violet}{\bf{ - \frac{3 \sqrt{3} - 6 + 6 - 4 \sqrt{3} }{ - 2} }}}$

${ \color{violet}{\bf{ - \frac{3 \sqrt{3} - 4 \sqrt{3} }{ - 2} }}}$

${ \color{violet}{\bf{ - \frac{ - \sqrt{3} }{ - 2} }}}$

${ \color{violet}{\bf{ - \frac{\cancel{ - \sqrt{3} }}{\cancel{ - 2}} }}}$

${ \color{violet}{\bf{\boxed{ - \frac{ \sqrt{3} }{2} }}}}$

$\pink{ \boxed{{\mathbb{ATT: ARMANDO}}}}$