Question 939615
The trigonometric functions cotangent and cosecant are defined as follows:
{{{cot(theta)=cos(theta)/sin(theta)}}} and {{{csc(theta)=1/sin(theta)}}} .
An important trigonometric identity is
{{{(sin(theta))^2+(cos(theta))^2=1}}} .
It is often written as {{{sin^2(theta)+cos^2(theta)=1}}} ,
and we understand that the exponent {{{2}}} written on the function means the value of the function squared.
 
Knowing all that (and a little algebra),
{{{1+cot^2(theta)=1+(cot(theta))^2=1+(cos(theta)/sin(theta))^2=1+(cos(theta))^2/(sin(theta))^2=((sin(theta))^2+(cos(theta))^2)/(sin(theta))^2=1/(sin(theta))^2=(1/sin(theta))^2=(csc(theta))^2}}}