(C3) Show that 4csc^2(x) - cot^2(x) = k can be expressed as sec^2(x) = (k-1)/(k-4) where k != 4

The student can answer this in several ways. One using the simple, known identities csc= 1/sin, cot=1/tan, sec=1/cos, tan=sin/cos, sin^2 + cos^2 = 1 and basic algebra is the following:
4csc^2 - cot^2 = k4/sin^2 - 1/tan^2 = k Substitute inverse fomulae4/sin^2 - cos^2/sin^2 = k Substitute tan4 - cos^2 = ksin^2 4 - cos^2 = k(1-cos^2) Write in terms of Coskcos^2 - cos^2 = k - 4cos^2(k - 1) = k-4 Gather Cos terms(k-1)/(k-4) = sec^2 Write in terms of inverses

FH
Answered by Fearghus H. Maths tutor

3562 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the first derivative of the line equation y=x^3 + 4


Suppose that you go to a party where everyone knows at least one other person, you get a bit bored and wonder whether there are at least two people which know the same number of people there.


I can differentiate exponentials (e^x), but how can I differentiate ln(x)?


Can you prove to me why cos^2(X) + sin^2(X) = 1?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning