<s>[INST] Evaluating $\sin\left(\arccos\frac12+\arccos\frac{7}{25}\right)$ 
Evaluate $$\sin\left(\arccos\frac12+\arccos\frac{7}{25}\right)$$

I know that $\arccos\frac12$ is $60^\circ$. I don't know how to continue.
 [/INST] $$\sin\left(\arccos\frac12+\arccos\frac{7}{25}\right)=$$
$$\sin(x+y) = \sin x \cos y + \cos x \sin y$$
Where $$x=\arccos\frac12$$ and $$y=  \arccos\frac{7}{25}$$
Note that $$ \cos x =\frac {1}{2}$$ and $$ \cos y =\frac {7}{25}$$ 
We can find $$ \sin x= {\sqrt 3}/2 $$ and $$\sin y = 24/{25}$$
upon substitution we get $$\sin\left(\arccos\frac12+\arccos\frac{7}{25}\right)=$$
$$        {7\sqrt 3}/50 +24/{50} = \frac { 7\sqrt 3 + 24}{50}    $$
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