Using your knowledge of complex numbers, such as De Moivre's and Euler's formulae, verify the trigonometric identities for the double angle.

de Moivre's: (cos(x)+isin(x))n=cos(nx)+isin(nx) set n=2 (cos(x)+isin(x))2=cos2(x)+2isin(x)cos(x)-sin2(x), which, according to de Moivre's cos2(x)+2isin(x)cos(x)-sin2(x)=cos(2x)+isin(2x) We notice that on both the RHS and LHS we have real and complex terms, which means that the real part on one side is equal to the real part of the other, and the same stands for the imgainary bits: cos(2x)=cos2(x)-sin2(x) sin(2x)=2sin(x)cos(x) These identities are the correct ones.

CP
Answered by Cezar P. Further Mathematics tutor

3459 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the shortest distance between the lines r = (1, 5, 6) + y(-2, -1, 0) and r = (1, 7, -3) + z(2, 0, 4)


The set of midpoints of the parallel chords of an ellipse with gradient, constant 'm', lie on a straight line: find its equation; equation of ellipse: x^2 + 4y^2 = 4


Find the modulus and argument of the complex number 1+2i


The curve C has parametric equations x=cos(t)+1/2*sin(2t) and y =-(1+sin(t)) for 0<=t<=2π. Find a Cartesian equation for C. Find the volume of the solid of revolution of C about the y-axis.


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences