Question

Ayuda porfavor, con todo su desarrollo.

Answer 1

PROBLEMA 1

[tex]Tg(x-30°) \times Ctg(2x-40°)=1 \\ [/tex]

[tex]x - 30° = 2x - 40° \\ - 30° + 40° = 2x - x \\ 10° = x[/tex]

☆ Calculamos "Tg3x" :

[tex]Tg(3x) = Tg(3 \times 10°) = Tg \: 30° = \frac{1}{ \sqrt{3} } = \frac{ \sqrt{3} }{3} \\ [/tex]

PROBLEMA 2

[tex]Sec2x=Csc(x+30°)[/tex]

[tex]2x + x + 30° = 90° \\ 3x + 30° = 90° \\ 3x = 90° - 30° \\ 3x = 60° \\ x = \frac{60°}{3} \\ x = 20°[/tex]

☆ Calculamos el valor de "E" :

[tex]E= \frac{Tg4x}{Ctg(x-10°)} + \frac{Sen(x + 10°)}{Cos3x} \\ E=\frac{Tg(4 \times 20°)}{Ctg(20°-10°)} + \frac{Sen(20° + 10°)}{Cos(3 \times 20°)} \\ E=\frac{Tg80°}{Ctg10°} + \frac{Sen30°}{Cos60°} \\ E = \frac{Tg80°}{Tg80°} + \frac{Sen30°}{Sen30°} \\ E = 1 + 1 \\ E = 2[/tex]