Question

(tanx+cosx)/senx=secx+cotx

Answer 1

 

tenemos nuestra identidad

 

$<var>\frac{tan(x)+cos(x)}{sen(x)}=sec(x)+cot(x)\\ \frac{tan(x)}{sen(x)}+\frac{cos(x)}{sen(x)}=sec(x)+cot(x)\\ \\ \frac{\frac{sen(x)}{cos(x)}}{sen(x)}+\frac{cos(x)}{sen(x)}=sec(x)+cot(x)\\ \\ \frac{1}{cos(x)}+\frac{cos(x)}{sen(x)}=sec(x)+cot(x)</var>$

 

sabemos que

 

$<var>\frac{1}{cos(x)}=sec(x)\\ \\ \frac{cos(x)}{sen(x)}=cot(x) </var>$

 

asi que 

$<var>\frac{1}{cos(x)}+\frac{cos(x)}{sen(x)}=sec(x)+cot(x)\\ \\ sec(x)+cot(x)=sec(x)+cot(x)</var>$