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Math Help - Trigonometric Function prove Problem

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    Trigonometric Function prove Problem

    If Sin 2\theta \ne 0 prove that \frac{sin3\theta}{sin\theta} - \frac{cos3\theta}{cos\theta} = 2 .hence or otherwise,Show that \frac{sin^{2}3\theta}{sin^{2}\theta} - \frac{cos^{2}3\theta}{cos^{2}\theta} = 8cos 2\theta
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    Re: Trigonometric Function prove Problem

    Quote Originally Posted by mastermin346 View Post
    If Sin 2\theta \ne 0 prove that \frac{sin3\theta}{sin\theta} - \frac{cos3\theta}{cos\theta} = 2 .hence or otherwise,Show that \frac{sin^{2}3\theta}{sin^{2}\theta} - \frac{cos^{2}3\theta}{cos^{2}\theta} = 8cos 2\theta
    You should know that \displaystyle \sin{(\alpha \pm \beta)} \equiv \sin{(\alpha)}\cos{(\beta)} \pm \cos{(\alpha)}\sin{(\beta)} and \displaystyle \cos{(\alpha \pm \beta)} \equiv \cos{(\alpha)}\cos{(\beta)} \mp \sin{(\alpha)}\sin{(\beta)}

    Here use \displaystyle \sin{(3\theta)} = \sin{(2\theta + \theta)} and \displaystyle \cos{(3\theta)} = \cos{(2\theta + \theta)}
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