<s>[INST] Calculating the value of $\cos \left(\frac{1}{2} \arccos \frac{3}{5}\right)$ I need help finding the value of $$\cos \left(\frac{1}{2} \arccos \frac{3}{5}\right)$$
My try:
let $\theta = \frac{1}{2} \arccos \frac{3}{5}$, then $2\theta = \arccos \frac{3}{5}$ and $\theta \in [0,\frac{\pi}{2}]$
Now let $A = 2\theta$, and $A \in [0,\frac{\pi}{2}]$ So $\cos A = \frac{3}{5} $ and $\sin A = \frac{4}{5} $. I noticed that I got stuck and wasn't getting closer to the answer.
Can someone please give me a HINT AND NOT THE ANSWER? Thanks.
 [/INST] Hint with a trigonometric identity:
$$\cos x=2\cos^2\frac x2-1$$
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