sin^2 (x) +sin^2 (2x) = sin^2 (3x)

Question

sin^2 (x) +sin^2 (2x) = sin^2 (3x)

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Philomena 5 years 2020-10-18T04:26:54+00:00 1 Answers 90 views 0

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  1. Vodka
    0
    2020-10-18T04:28:43+00:00
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    PT $\Leftrightarrow \dfrac{1-\cos2x+1-\cos4x}{2}=\dfrac{1-\cos6x}{2}$

    $\Leftrightarrow \cos2x+\cos4x-\cos6x=1$

    $\Leftrightarrow 2\sin4x.\sin2x+\cos4x=1$

    $\Leftrightarrow 2\sin4x.\sin2x-2\sin^22x=0$

    $\Leftrightarrow \sin4x.\sin2x-\sin^22x=0$

    $\Leftrightarrow \sin2x(\sin4x-\sin2x)=0$

    $\Leftrightarrow 2\sin2x.\cos3x.\sin x=0$

    $+) \sin 2x=0\Leftrightarrow x=\dfrac{k\pi}{2}$

    $+) \cos3x=0\Leftrightarrow x=\dfrac{\pi}{6}+\dfrac{k\pi}{3}$

    $+) \sin x=0\Leftrightarrow x=k\pi$

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