verificar 2+sec(a)cos(a)=3

Solución

verificar

2 + sec (a) cos (a) = 3

Verdadero

Pasos de solución

2 + sec (a) cos (a) = 3

Manipular el lado derecho

2 + sec (a) cos (a)

Expresar con seno, coseno

2 + cos (a) sec (a)

Utilizar la identidad trigonométrica básica:

sec (x) = \frac{1}{cos ( x )}

= 2 + cos (a) \frac{1}{cos ( a )}

2 + cos (a) \frac{1}{cos ( a )} = 3

2 + cos (a) \frac{1}{cos ( a )}

cos (a) \frac{1}{cos ( a )} = 1

cos (a) \frac{1}{cos ( a )}

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot cos ( a )}{cos ( a )}

Eliminar los terminos comunes:

cos (a)

= 1

= 2 + 1

Simplificar

= 3

= 3

= 3

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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