Calculus Practise: Complex Numbers & Trigonometry Proof

Test Preparation
1

<p>Here is the question: Prove that cos 4θ = 8cos^4 (θ] – 8cos^2 (θ] + 1 <a href=“sorry%20about%20the%20different%20brackets…%20if%20I%20use%20a”>i</a> it comes up with some strange symbols…)*</p>

<p>Once you have tried it, you can find the full proof here - [Complex</a> Numbers & Trigonometry Question](<a href=“http://www.rumchev.com/notes/calculus/Complex%20Numbers%20&%20Trigonometry%20Question.pdf]Complex”>http://www.rumchev.com/notes/calculus/Complex%20Numbers%20&%20Trigonometry%20Question.pdf)</p>

2

<p>well, an easier proof is just to see that cos2x=2(cosx)^2-1. so by expanding cos4x using this trig identity, the desired answer follows.</p>