Using the equation cos(a+b) = cos(a)cos(b) - sin(a)sin(b) or otherwise, show that cos(2x) = 2cos^2(x) - 1.

First let a = b = x such that:          

          cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

becomes:

          cos(x + x) = cos(x)cos(x) - sin(x)sin(x)

Leading to:

          cos(2x) = cos2(x) - sin2(x)

Using the fact that sin2(y) + cos2(y) = 1 or rearranged sin2(y) = 1 - cos2(y):

          cos(2x) = cos2(x) - (1 - cos2(y)) = 2cos2(x) - 1, as required.

Another suitable approach may involve the Maclaurin series of cos(2x) and cos2(x) to arrive at the required relation, although this is more involved.

BH
Answered by Benjamin H. Maths tutor

3487 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve the following: sinx - cosx = 0 for 0≤x≤360


Differentiate, with respect to x, e^3x + ln 2x,


The curve C has equation y=3x^3-11x+1/2. The point P has coordinates (1, 3) and lies on C . Find the equation of the tangent to C at P.


Find the stationary points and their nature of the curve y = 3x^3 - 7x + 2x^-1


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences