First of all, I assume that when you saythat you are actually saying : sec(θ)=5 and tan(θ)=2√6.sec = 5, tan = 2*sqrt(6)

a) Correct.cos(θ)=1/sec(θ)=1/5

b) Correct.cot(θ)=1/tan(θ)=1/(2√6)= √6/12

Assume that 90 is in degrees.

c)cot(90-θ)=tan(θ)= 2√6

d)tan(θ)=sin(θ)/cos(θ)

sin(θ)=tan(θ)cos(θ)

sin(θ)=( 2√6)(1/sec(θ))

sin(θ)= ( 2√6)(1/5)

sin(θ)= (2√6)/5

a)cot(θ)=(√3/3)multiply that by(√3/√3)you get

1/√3

cot(θ) is u/v, you take it from there? Does your teacher want all possible values of θ or just one?

b) is correct if you are looking for just one value of θ.

hope that helped.