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The value of $\cot θ - \tan θ - 2 \tan 2 θ - 4 \tan 4 θ - 8 \cot 8 θ$ is

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a

0

b

1

c

-1

d

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detailed solution

Correct option is A

We know that∴ cot⁡α−tan⁡α=2cot⁡2αcot⁡θ−tan⁡θ−2tan⁡2θ−4tan⁡4θ−8cot⁡8θ=2cot⁡2θ−2tan⁡2θ−4tan⁡4θ−8cot⁡8θ=2(2cot⁡4θ)−4tan⁡4θ−8cot⁡8θ=4cot⁡4θ−4tan⁡4θ−8cot⁡8θ=4(cot⁡4θ−tan⁡40)−8cot⁡8θ=4×2cot⁡8θ−8cot⁡8θ=0

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