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
DS
Related Maths A Level answers
All answers ▸How do I find the maxima and minima of f(x) = e^(x^2)?
Differentiate with respect to x. y(x) = e^(7x^2)
Solve 2sec^2(x) = 3 + tan(x) for 0 < x <pi/2
How do you find the angle between two lines in three dimensional vector space given two points on line 1 and the vector equation of line 2