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tan21∘+tan23∘+tan25∘+⋯+tan287∘+tan289∘= ?\large \tan^2 1^\circ + \tan^2 3^\circ + \tan^2 5^\circ + \cdots+ \tan^2 87^\circ + \tan^2 89^\circ = \ ? tan21∘+tan23∘+tan25∘+⋯+tan287∘+tan289∘= ?
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sec(π10)sec(3π10)sec(7π10)sec(9π10)= ?\large \sec \left ( \dfrac {\pi}{10} \right ) \sec \left ( \dfrac {3\pi}{10} \right ) \sec \left ( \dfrac {7\pi}{10} \right ) \sec \left ( \dfrac {9\pi}{10} \right ) = \; ?sec(10π)sec(103π)sec(107π)sec(109π)=?
12x=cos(a)cos(2a)cos(3a)⋯cos(999a)\large \dfrac1{2^x} = \cos (a) \cos(2a) \cos(3a) \cdots \cos(999a) 2x1=cos(a)cos(2a)cos(3a)⋯cos(999a)
The equation above holds true for a=2π1999a = \dfrac{2\pi}{1999} a=19992π. Find xxx.
tanπ7tan2π7tan3π7=A\large \tan\frac{\pi}{7}\tan\frac{2\pi}{7}\tan\frac{3\pi}{7}= \sqrt{A} tan7πtan72πtan73π=A Find AAA.
f(x)=cos(x)⋅cos(2x)⋅cos(3x)⋯cos(999x)\large f(x) = \cos(x) \cdot \cos(2x) \cdot \cos(3x)\cdots \cos(999x)f(x)=cos(x)⋅cos(2x)⋅cos(3x)⋯cos(999x)
If f(2π1999)=12kf \left(\dfrac{2\pi }{1999}\right) = \dfrac{1}{2^{k}}f(19992π)=2k1, find kkk.
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