Question

Determine o valor numérico de A= cos2.x - cotg (9/4 x) sobre sen x/2 + tg (9/4 x)
com x= pi/3 rad

Answer 1

1Rad=180º

x= \dfrac{180}{3}=60\º

Com o radiano transformado em grau ,Vamos substituir na expressão trigonométrica.

A= \dfrac{Cos(2x)-cotg (\frac{9}{4}x) }{Seno (\frac{x}{2})-Tg (\frac{9}{4}x)} \\\\\\\\
A= \dfrac{Cos(2.60)-cotg (\frac{9}{4}.60) }{Seno (\frac{60}{2})-Tg (\frac{9}{4}60)}\\\\\

Organizando a expressao.\\\\\

A= \dfrac{Cos(120\º)-cotg (135\°) }{Seno (30\º)-Tg (135\º)}\\\\\\\\
 A= \dfrac{ -\frac{1}{2}-(-1) }{(\frac{1}{2})-(-1)}\\\\\\\
A= \frac{- \frac{1}{2}+1 }{ \frac{1}{2}+1 }\\\\\\\
A= \dfrac{ -\dfrac{1}{2} }{ \dfrac{3}{2} }

Conserva a primeira e multiplica pelo inverso da egunda.

A= -\dfrac{1}{2}. \dfrac{2}{3} \\\\\\
A= -\dfrac{1}{3} 




\boxed{Resposta: A= -\frac{1}{3} }