tenemos
[tex]\frac{tan(x)+cos(x)}{sen(x)}=sec(x)+cot(x)\\ \\ \frac{\frac{sen(x)}{cos(x)}+cos(x)}{sen(x)}=sec(x)+cot(x)\\ \\ \frac{\frac{sen(x)}{cos(x)}}{sen(x)}+\frac{cos(x)}{sen(x)}=sec(x)+cot(x)\\ \\ \frac{1}{cos(x)}+\frac{cos(x)}{sen(x)}=sec(x)+cot(x)[/tex]
sabemos que:
[tex]\frac{1}{cos(x)}=sec(x)\\ \\ \\ \frac{cos(x)}{sen(x)}=cot(x)[/tex]
por lo que...
[tex]\frac{1}{cos(x)}+\frac{cos(x)}{sen(x)}=sec(x)+cot(x)\\ \\ sec(x)+cot(x)=sec(x)+cot(x)[/tex]
saludos.