Using the identity cos(A+B)= cosAcosB-sinAsinB, prove that cos2A=1-2sin^2A.

Use cos(A+B)=cosAcosB-sinAsinB and let A=B so cos(A+A)=cosAcosA-sinAsinA this means cos(2A)=cos2A-sin2A and since cos2A+sin2A=1, cos2A=1-sin2A. Therefore, by subbing cos2A=1-sin2A into cos(2A)=cos2A-sin2A, we get cos(2A)=1-sin2A-sin2A=1-2sin2A.

Answered by Rebecca F. Maths tutor

19893 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve x(5(3^0.5)+4(12^0.5))=(48^0.5) to the simplest form. (4 Marks)


Find the derivative of y = 3x^4 - 10x^2+7x


How can I find all the solutions to cos(3x) = sqrt(2)/2 for 0<=x<=2pi ?


What is the differential of (14x^3-3x^2)^3


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