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$f (x) = \frac{\sin x + \sin 3 x + \sin 5 x + \dots + \sin 15 x}{\cos x + \cos 3 x + \cos 5 x + \dots + \cos 15 x} then the value of f (x) at x = \frac{π}{32}$

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Correct option is A

sinα+sin(α+d)+….+sinα+(n-1)d==sinnd2sind2sinα+α+(n-1)d2andcosα+cos(α+d)+….+cos(α+(n-1)d)==sinnd2sind2cos(α+α+(n-1))d)2∴sinx+sin3x+….+sin15xcosx+cos3x+….+cos15x=sinx+15x2cosx+15x2=tan8x ∴fπ32=tan8π32=1

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f(x)=sinx+sin3x+sin5x+…+sin15xcosx+cos3x+cos5x+…+cos15x then the value of f(x) at x=π32

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$f (x) = \frac{\sin x + \sin 3 x + \sin 5 x + \dots + \sin 15 x}{\cos x + \cos 3 x + \cos 5 x + \dots + \cos 15 x} then the value of f (x) at x = \frac{π}{32}$