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Question

Simplify $$\displaystyle \sqrt{2+\sqrt{2+2\cos \left ( \pi +60^{0} \right )}}$$


Solution

$$\displaystyle \sqrt{2+\sqrt{2+2\cos \left ( \pi +60^{0} \right )}}$$
$$\displaystyle =\sqrt{2+\sqrt{2-2\cos 60^{0}}}$$
$$\displaystyle \left ( because \cos \left ( \pi +\theta  \right )=-\cos \theta  \right )$$
$$\displaystyle =\sqrt{2+\sqrt{2-2\times \frac{1}{2}}}$$
$$\displaystyle =\sqrt{2+\sqrt{1}}=\sqrt{3}$$

Mathematics

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