The value of tan-2 tan 2 -4 tan 4 -8 tan 8 -16 16 - is

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Sum of n Terms

The value of ...

Question

The value of $t a n α + 2 t a n 2 α + 4 t a n 4 α + 8 t a n 8 α + 16 c o t 16 α$ is

c o t α

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c o s α

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c o t 2 α

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t a n 2 α

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Solution

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tan α + 2 tan 2 α + 4 tan 4 α + 8 tan 8 α + 16 cot 16 α = cot α

cot α - tan α = 2 cot 2 α

tan α + 2 tan 2 α + 4 tan 4 α + 8 cot 8 α - cot α

tan α + 2 tan 2 α + 4 tan 4 α + 8 cot 8 α =

The value of $t a n α + 2 t a n (2 α) + 4 t a n (4 α) + . . . . . + 2^{n - 1} t a n (2^{n - 1} α) + 2^{n} c o t (2^{n} α)$ is

cot α - tan α - 2 tan 2 α - 4 tan 4 α = 8 cot 8 α .

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