Question 627972
Since {{{tan(theta)=sin(theta)/cos(theta)}}} and {{{cot(theta)=cos(theta)/sin(theta)}}} ,
{{{tan(theta)+cot(theta)=sin(theta)/cos(theta)+cos(theta)/sin(theta)}}}
For a common denominator to add those two fractions, the obvious choice is {{{sin(theta)cos(theta)}}} , so
{{{tan(theta)+cot(theta)=sin^2(theta)/sin(theta)cos(theta)+cos^2(theta)/sin(theta)cos(theta)}}}
Now we can write it all as one fraction:
{{{tan(theta)+cot(theta)=(sin^2(theta)+cos^2(theta))/sin(theta)cos(theta)}}}
At this point, you can use the identity {{{sin^2(theta)+cos^2(theta)=1}}} to conclude that
{{{tan(theta)+cot(theta)=1/sin(theta)cos(theta)}}}