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

3396 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Given that y = cosh^-1 (x) , Show that y = ln(x+ sqrt(x^2-1))


Integral of ln x


How would go about finding the set of values of x for which x+4 > 4 / (x+1)?


How can we describe complex numbers ?


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