How can I write the following as a single trig function?
$$2\cos^2\left(\frac{\pi}6\right) – 1$$
To attempt this, I looked at all the identities (sum & difference, double angle identities, and Pythagorean identities)** and the identity that seemed fitting was the Pythagorean identity specifically $\sin^2\theta + \cos^2\theta = 1$.
I used this identity to isolate $\cos^2\theta$, but then I found myself using it over and over again; it was alternating between subbing in sine squared and cosine squared. (I didn't bother to post the work, but I can if it's needed.)
How should I get the textbook answer of $\cos \frac{\pi}3$?
A hint to an approach I might've missed would be grateful! 🙂
**I've been merely taught the three identities listed. Unfortunately, I can't identify any other methods mentioned in the answers.
Best Answer
$\cos (a+b)=\cos \,a \cos \, b-\sin \,a \sin \,b$. Put $a=b$ to get $\cos(2a)=\cos^{2}(a)-\sin^{2}(a)=2\cos^{2}(a)-1$. Put $a= \frac {\pi} 6$