English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

verificar 5sec^2(x)+4=9sec^2(x)-4tan^2(x)

Solución

verificar

5 sec^{2} (x) + 4 = 9 sec^{2} (x) - 4 tan^{2} (x)

Verdadero

Pasos de solución

5 sec^{2} (x) + 4 = 9 sec^{2} (x) - 4 tan^{2} (x)

Manipular el lado izquierdo

9 sec^{2} (x) - 4 tan^{2} (x)

Re-escribir usando identidades trigonométricas

9 sec^{2} (x) - 4 tan^{2} (x)

Utilizar la identidad pitagórica:

tan^{2} (x) + 1 = sec^{2} (x)

tan^{2} (x) = sec^{2} (x) - 1

= 9 sec^{2} (x) - 4 (sec^{2} (x) - 1)

Simplificar

9 sec^{2} (x) - 4 (sec^{2} (x) - 1) : 5 sec^{2} (x) + 4

9 sec^{2} (x) - 4 (sec^{2} (x) - 1)

Expandir

- 4 (sec^{2} (x) - 1) : - 4 sec^{2} (x) + 4

- 4 (sec^{2} (x) - 1)

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = - 4, b = sec^{2} (x), c = 1

= - 4 sec^{2} (x) - (- 4) \cdot 1

Aplicar las reglas de los signos

- (- a) = a

= - 4 sec^{2} (x) + 4 \cdot 1

Multiplicar los numeros:

4 \cdot 1 = 4

= - 4 sec^{2} (x) + 4

= 9 sec^{2} (x) - 4 sec^{2} (x) + 4

Sumar elementos similares:

9 sec^{2} (x) - 4 sec^{2} (x) = 5 sec^{2} (x)

= 5 sec^{2} (x) + 4

= 5 sec^{2} (x) + 4

= 5 sec^{2} (x) + 4

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero