Math(Correction)
posted by Mark .
Use the given function values and trigonometric identities (including the relationship between a trigonometric function and its cofunction of a complementary angle) to find the indicated trigonometric functions.
sec Q = 5
tan Q = 2sqrt6
a) cos Q
b) cotQ
c) cot(90 degrees  Q)
d) sin Q

Ok, finally , now it makes sense
And now it is easy.
given: secQ = 5, then cosQ = 1/5
So we have a right angles triangle, where the hypotenuse is 5, the side adjacent to angle Q is 1, and the opposite to angle Q is 2√6
Notice that the second function, tanQ = 2√6 was not necessary, since we can see that from our triangle.
a) cosQ = 1/5
b) cotQ = 1/tanQ = 1/(2√6)
c) cot(90  Q) = tan Q = 2√6
d) sinQ = 2√6/5 
SIN(90Q)/COSEC(90Q)=COS(90Q)/COSEC(90Q)

SIN(90Q)/COSEC(90Q)+COS(90Q)/COSEC(90Q)=1