- #1

brotherbobby

- 699

- 163

- Homework Statement
- Show that ##\large{\boxed{\tan\theta+2\tan 2\theta+4\tan 4\theta+8 \cot 8\theta = \cot\theta}}##

- Relevant Equations
- 1. ##\tan 2\theta = \frac{2\tan\theta}{1-\tan^2\theta}##

2. ##\tan 4\theta = \frac{4\tan \theta-4\tan^3 \theta}{1-6\tan^2\theta+\tan^4\theta}## (borrowed from a problem that asked to prove as much).

3. ##\tan 8\theta =?, \cot 8\theta = ?## (No readymade equations available)

**Let me copy and paste the problem as it appears in the text :
Problem Statement : **

**Attempt :**I haven't been able to make any significant attempt at solving this problem, am afraid. I tried to reduce all the higher submultiple angles ##2\theta, 4\theta, 8\theta## into ##\theta##, but the resulting equation became unwieldy.

**Request :**As I have failed to do my fair share, the barest of hints to start me off would be welcome.