<s>[INST] Can someone show me how to simplify $\sin\left(\arccos\left(\frac{x}{x+1}\right)\right)$ I am needing help learning how to simplify the following equation: 
$$\sin\left(\arccos\left(\frac{x}{x+1}\right)\right)$$
Also any steps on how to get the answer would be greatly appreciated!
 [/INST] as Rahul said... let $\arccos(\frac{x}{x+1})=\theta$ so $\cos\theta=\frac{x}{x+1}$ but you want $\sin\theta$ which is $\sqrt{1-\cos^2\theta}$.


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*Remember $\arccos t$ is between $0$ and $\pi$, so $\sin(\arccos t)$ is positive. 


so the answer would be $$\sqrt{1-(\frac{x}{x+1})^2}=\sqrt{1-\frac{x^2}{(x+1)^2}}=\sqrt{\frac{(x+1)^2-x^2}{(x+1)^2}}=\sqrt{\frac{2x+1}{(x+1)^2}}=\frac{\sqrt{2x+1}}{x+1}.$$
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