Question

Demostrar sacando el mismo valor

Answer 1

Respuesta:

Explicación paso a paso:

Debemos saber antes que:

$sec(\theta)=\frac{1}{cos(\theta)}\\\\tan(\theta)=\frac{sen(\theta)}{cos(\theta)}\\\\sen(-\theta)=-sen(\theta)\\\\cos(-\theta)=cos(\theta)\\\\tan^2(\theta)+1=sec^2(\theta)$

Resolvemos el lado izquierdo:

$sen(-\theta)tan(-\theta)sec(-\theta)+1=sec^2(\theta)\\\\sen(-\theta)\times \frac{sen(-\theta)}{cos(-\theta)}\times\frac{1}{cos(-\theta)}+1=sec^2(\theta)\\\\\frac{sen(-\theta)\times sen(-\theta)}{cos(-\theta)\times cos(-\theta)}+1=sec^2(\theta)\\\\\frac{-sen(\theta)\times -sen(\theta)}{cos(\theta)\times cos(\theta)}+1=sec^2(\theta)\\\\\frac{sen^2(\theta)}{cos^2(\theta)}+1=sec^2(\theta) \\\\tan^2(\theta)+1=sec^2(\theta)\\\\sec^2(\theta)=sec^2(\theta)$\