Question

x= cos A + cos 2A + cos 3A
y=sin A+sin 2A + sin 3A => x/y =​

Answer 1

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$x = cos3a + cosa + cos2a \\ x = 2cos( \frac{3a + a}{2} )cos( \frac{3a - a}{2} ) + cos2a \\ x = 2cos(2a)cos(a) + cos2a \\ x = cos2a(2cosa + 1) \\ y = sin3a + sina + sin2a \\ y = 2sin( \frac{4a}{2} )cos( \frac{2a}{2} ) + sin2a \\ y = 2sin2acosa + sin2a \\ y = sin2a(2cosa + 1) \\ \\ \frac{x}{y} = \frac{cos2a(2cosa + 1)}{sin2a(2cosa + 1)} \\ \frac{x}{y} = cot2a$