Question 678960
{{{(cot (theta)+tan (theta))/cot (theta)=sec^2 (theta)}}}

start with left side and prove that is equal to right side

use identities:

{{{tan(theta)=  sin(theta)/cos(theta)}}}	 


{{{cot(theta)= 1/tan(theta)= cos(theta)/sin(theta)}}}


so,

{{{cot (theta)/cot(theta)+tan(theta)/cot(theta)}}}


={{{1+(sin(theta)/cos(theta))/(cos(theta)/sin(theta))}}}



={{{1+(sin(theta)sin(theta))/(cos(theta)cos(theta))}}}


={{{1+(sin^2 (theta))/(cos^2 (theta) )}}}


={{{1+(sin^2 (theta))/(cos^2(theta) )}}}


={{{1 + tan^2(theta)}}}........use identity  {{{1 + tan^2(theta)= sec^2(theta)}}} 


={{{sec^2(theta)}}}