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Объяснение:

[tex]tg a + ctg a + tg 3a + ctg 3a = \frac{sin\alpha }{cos\alpha } +\frac{cos\alpha }{sin\alpha } +\frac{sin3\alpha }{cos3\alpha } +\frac{cos3\alpha }{sin3\alpha } =\\\\=\frac{sin\alpha *cos3\alpha +cos\alpha *sin3\alpha }{cos\alpha *cos3\alpha } + \frac{sin\alpha *cos3\alpha +cos\alpha *sin3\alpha }{sin\alpha *sin3\alpha } =\\\\[/tex]

[tex]=\frac{sin\alpha *sin3\alpha *sin4\alpha +cos\alpha *cos3\alpha *sin4\alpha }{sin\alpha *cos\alpha *sin3\alpha *cos3\alpha } = \frac{sin4\alpha *(sin\alpha sin3\alpha +cos\alpha*cos3\alpha) }{0.5*sin2\alpha *0.5*sin6\alpha } =\\\\=\frac{4*2*sin2\alpha *cos2\alpha *cos2\alpha }{sin2\alpha*sin6\alpha } = \frac{8*cos^22\alpha }{sin6\alpha }[/tex]

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