Question

Cos theta + sin theta tan theta = sec theta

Answer 1

Hola.

Identidades a considerar

$sec(\alpha)=\frac{1}{cos(\alpha)}$

$tan(\alpha)=\frac{sen(\alpha)}{cos(\alpha)}$

$sen^{2}(\alpha )+cos^{2}(\alpha) = 1$

Desarrollamos

$cos(\alpha)+sen(\alpha)*tan(\alpha)=sec(\alpha)$

$cos(\alpha)+sen(\alpha)*\frac{sen(\alpha)}{cos(\alpha)} = sec(\alpha)$

$cos(\alpha)+\frac{sen^{2}(\alpha)}{cos(\alpha)}=sec(\alpha)$

$\frac{cos(\alpha)*cos(\alpha)+sen^{2}(\alpha)}{cos(\alpha)}=sec(\alpha)$

$\frac{cos^{2}(\alpha)+sen^{2}(\alpha)}{cos(\alpha)} = sec(\alpha)$

$\frac{1}{cos(\alpha)}=sec(\alpha)$

$sec(\alpha)=sec(\alpha)$       $//$  $identidad$ $verdadera$

Un cordial saludo