MathDB

1

Part of 2017 ISI Entrance Examination

Problems(1)

$\tan(n\theta)$ is rational

Source: BStat-BMath 2017: problem 1

5/14/2017
Let the sequence {an}n≥1\{a_n\}_{n\ge 1} be defined by an=tan⁡(nθ)a_n=\tan(n\theta) where tan⁡θ=2\tan\theta =2. Show that for all nn, ana_n is a rational number which can be written with an odd denominator.
algebra