1 + 5sin^2x= 7sin^2x solve trig equation. Can you show me how to solve this trig equation?

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1 + 5sin^2x= 7sin^2x solve trig equation. Can you show me how to solve this trig equation?

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  1. Ava
    0
    2021-09-09T16:53:04+00:00

    Answer: x = \frac{\pi}{4}\pm k\frac{\pi}{2}\,\,\,\,\,\,k=\{0,1,2,...\}

    Step by step:

    1 + 5\sin^2x= 7\sin^2x\\\sin^2 x\rightarrow z\\1 + 5z = 7z\\2z = 1\\z = \frac{1}{2}\implies \sin^2 x = \frac{1}{2}\\|\sin x| = \frac{1}{\sqrt{2}}\\\sin x = \pm\frac{1}{\sqrt{2}}=\pm\frac{\sqrt{2}}{2}\\\implies x = \frac{\pi}{4}\pm k\frac{\pi}{2}\,\,\,\,\,\,k=\{0,1,2,...\}

    (Used a table of common angles)

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