To display equations, I recently installed LaTeX into WordPress by using a Latexrender plugin and it works great! I am going to try it out by blogging about a relatively easy way to derive the double angle formulas for the sine and cosine. The double angle formulas relate and to and .
Let’s be honest, who wants to waste their cortical space remembering formulas like this. Instead, you can derive them pretty easily by remembering a few more elementary facts. First, you can write any complex number as:
Next, you must remember how to work with exponents:
Now we put it all together.
We start by writing
We then square both sides
Now use the rule for exponents on the left-hand side, and multiply out the right-hand side:
Now write the left-hand side in terms of sines and cosines again:
Last, equate the real parts and the imaginary parts and you have your double-angle formulas:
Easy as !