Find the exact value of sine [2 cosine Superscript negative 1 Baseline (- StartFraction StartRoot 2 EndRoot/2 EndFraction )] = nothing

Question

Find the exact value of sine [2 cosine Superscript negative 1 Baseline (- StartFraction StartRoot 2 EndRoot/2 EndFraction )] = nothing

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Melody 3 months 2021-10-08T14:28:07+00:00 1 Answer 0 views 0

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    2021-10-08T14:29:12+00:00

    Answer:

    \frac{3\pi}{2}.

    Step-by-step explanation:

    The given expression is

    2\cos^{-1}\left(-\frac{\sqrt{2}}{2}\right)

    It can be rewritten as

    2\cos^{-1}\left(-\frac{1}{\sqrt{2}}\right)

    2\left [\pi-\cos^{-1}\left(\frac{1}{\sqrt{2}}\right)\right]            [\because \cos^{-1}(-x)=\pi-\cos^{-1}(x), x\in [-1,1]]

    2\left [\pi-\cos^{-1}\left(\cos \frac{\pi}{4}\right)\right]

    2\left [\pi-\frac{\pi}{4}\right]

    2\left [\frac{4\pi-\pi}{4}\right]

    \frac{3\pi}{2}

    Hence, the exact value of given expression is \frac{3\pi}{2}.

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