Given that 4(cosec x)^2 - (cot x)^2 = k, express sec x in terms of k.

This question makes good use of the trigonometric identities tan²x + 1 = sec²x and 1 + cot²x = cosec²x which can be easily recited in the exam by using the identity sin²x + cos²x = 1 and then dividing by cos²x or sin²x respectively!

Remember, the trick when it comes to solving problems such as these is just perseverance and using trial and error. Practice makes perfect!

There are many ways of solving this problem, here is one method:

4cosec²x - cot²x = k
4(1 + cot²x) - cot²x = k
4 + 3cot²x = k
3cot²x = k - 4
tan²x = 3 / (k - 4)
sec²x - 1 = 3 / (k - 4)
sec x = ( (3 / (k-4)) + 1 )^1/2