We have an answer to "Express sin⁡(arccos⁡(2x)) in terms of x."

zi2lalZ

Answered question

2021-09-01

Express

\sin (\arccos (\frac{2}{x}))

in terms of x.

diskusje5

Skilled2021-09-02Added 82 answers

\sin (\arccos (\frac{2}{x}))

\sin (\arccos (\frac{2}{x})) = \sin (\arcsin (\sqrt{1 - {(\frac{2}{x})}^{2}}))

\sin (\arccos (\frac{2}{x})) = \sin (\arcsin (\sqrt{1 - \frac{4}{x^{2}}}))

\sin (\arccos (\frac{2}{x})) = \sin (\arcsin (\sqrt{\frac{x^{2} - 4}{x^{2}}}))

Since,

\sin (\arccos (\frac{2}{x})) = \sqrt{\frac{x^{2} - 4}{x^{2}}}

Then,

\sin (\arccos (\frac{2}{x})) = \frac{\sqrt{x^{2} - 4}}{x}

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