# How do you prove that (1+tanx)/(sinx+cosx)=secx?

Feb 14, 2015

You can use the followings:
$\tan \left(x\right) = \sin \frac{x}{\cos} \left(x\right)$
$\sec \left(x\right) = \frac{1}{\cos} \left(x\right)$

Giving:

$\frac{1 + \sin \frac{x}{\cos} \left(x\right)}{\sin \left(x\right) + \cos \left(x\right)} = \frac{1}{\cos} \left(x\right)$

$\frac{\cos \left(x\right) + \sin \left(x\right)}{\cos} \left(x\right) \cdot \frac{1}{\sin \left(x\right) + \cos \left(x\right)} = \frac{1}{\cos} \left(x\right)$

simplifying:

$\frac{1}{\cos} \left(x\right) = \frac{1}{\cos} \left(x\right)$