Use angle sum ident to verify cos(2x)=2cos^2(x)-1

[adpcane15]

Use an angle sum identity to verify the identity cos 2Ө=2cos^2Ө-1

 

[skeeter]

sum identity for cosine is ...
cos(x+y) = cosx*cosy - sinx*siny

now, cos(2a) = cos(a+a) ... ball is in your court, play it.

 

[jonboy]

Hi adpcane!

I'm learning Trig myself but I think I've solved this one!

Since \(\displaystyle Cos\,2A\,=\,Cos\,(A\,+\,A)\) we can use: \(\displaystyle \L Cos\,(A\,+\,B)\,=\,CosA\,CosB\,-\,SinA\,SinB\)

Except we'll manipulate it to \(\displaystyle Cos\,(A\,+\,A)\)

\(\displaystyle \L 2cos^2A\,-\,1=\,CosA\,CosA\,-\,SinA\,SinA\)

This left side can be rewritten as:\(\displaystyle \L \;Cos^2A\,-\,Sin^2A\)

Since \(\displaystyle Cos\,(2A)\,=\,Cos^2A\,-\,Sin^2A\)

\(\displaystyle \L 2cos^2A\,-\,1=Cos\,(2A)\)