How do I show that (cos^4x - sin^4x) / cos^2x = 1 - tan^2x

Start with the LHS:

(cos^4x - sin^4x) / cos^2x 

Recognise the difference of two squares on the top line, which simplifies to (cos^2x - sin^2x)(cos^2x + sin^2x):

(cos^2x - sin^2x)(cos^2x + sin^2x) / cos^2x

Because of the identity sin^2x + cos^2x = 1, the second bracket (cos^2x + sin^2x) simplifies to 1:

(cos^2x - sin^2x) / cos^2x

Separate the two parts of the numerator:

(cos^2x / cos^2x) - (sin^2x / cos^2x)

These parts both simplify to 1 and tan^2x respectively:

1 - tan^2x 

= RHS

JM
Answered by Jack M. Maths tutor

18621 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Express Cosx-3Sinx in form Rcos(x+a) and show that cosx-3sinx=4 has no solution MEI OCR June 2016 C4


∫(3x+4)2dx


How do I use product rule when differentiating?


Find the set of values of x for which 3x^2+8x-3<0.


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