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Relationship between the Short Run Average and Marginal Cost Curves

13. Prove tha...

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13. Prove that tanx + 2tan2x + 4tan4x + 8cot8x = cotx

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\int (tan x + 2 tan 2 x + 4 tan 4 x + 8 cot 8 x) d x

tan x + 2 tan 2 x + 4 tan 4 x + 8 cot 8 x = \sqrt{3}

then the general solution of

x =

t a n x + c o t x = s e c x c o s e c x

\frac{d}{d x} [\frac{t a n x - c o t x}{t a n x + c o t x}] =

tanx + c o t x = s e c x . c o s e c x

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Relationship between the Short Run Average and Marginal Cost Curves

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