Explain the process of using de Moivre's Theorem to find a trigonometric identity. For example, express tan(3x) in terms of sin(x) and cos(x).

  1. Identify de Moivre's Theorem: (cos(x) + isin(x))n = cos(nx) + isin(nx) 2) Deduce the correct value of n for the given problem. In this example we set n=3 3) Expand the LHS (usually by a binomial expansion). In this example we have (cos(x) + isin(x))3 = cos3(x) + 3icos2(x)sin(x) - 3cos(x)sin2(x) - isin3(x) = cos(3x) + isin(3x) 4) Equate the real parts. Here we have cos(3x) = cos3(x) - 3cos(x)sin2(x) 5) Equate the imaginary parts. Here we have sin(3x) = 3cos2(x)sin(x) - sin3(x) 6) Use these results to derive identity. In this case we divide sin(3x) by cos(3x).
OL
Answered by Ollie L. Further Mathematics tutor

3260 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

if y = (e^x)^7 find dy/dx


Evaluate ∫sin⁴(x) dx by expressing sin⁴(x) in terms of multiple angles


Find the inverse of a 3x3 matrix


Given that x = i is a solution of 2x^3 + 3x^2 = -2x + -3, find all the possible solutions


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