Question

suppose csc x=5, cos x > 0, find cos x

Answer 1

you know
\[\csc(x)=5\] so right away you know that
\[\sin(x)=\frac{1}{5}\]

Answer 2

now the easiest thing to do is draw a right triangle with "opposite" side 1 and hypotenuse 5. the "adjacent" side will be
\[\sqrt{5^2-1^2}=\sqrt{24}\] so
\[\cos(x)=\frac{\sqrt{24}}{5}\]

Answer 3

you might want to write
\[\sqrt{24}=2\sqrt{6}\]