Question

tan 7 theta * tan 8 theta = 1, find the value of theta

Answer 1

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Given :-

tan7θ tan8θ = 1

To find :-

Value of θ

Identity used

$1. \: tanθ = \frac{1}{cotθ} \\ 2. \: if \: tanx \: = tany \\ = > \: x = \: n\pi + y$

Solution:-

$tan7θ \: tan8θ = 1 \\ tan7θ = \frac{1}{tan8θ} \\ tan7θ = cot8θ \\ tan7θ = tan( \frac{\pi}{2} - 8θ) \\ 7θ = n\pi \: + \frac{\pi}{2} - 8θ \\ 15θ = n\pi \: + \frac{\pi}{2} \\ θ = \frac{n\pi}{15} + \frac{\pi}{30} \\ = > θ = (n + \frac{1}{2} ) \frac{\pi}{15} \\ \: where \: n \: is \: an \: integer.$

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