Question

Heya Mates❤️

➡️ Prove that tan(π/16) + 2×tan(π/8) + 4 = cot(π/16) .

☑️Please provide proper solution.​

Answer 1

Answer:

tan(π/16) + 2×tan(π/8) + 4 = cot(π/16)

Hence Proved !!

❤️Hope it will help you.❤️

Answer 2

Answer:

$\green{ \huge \boxed{solution}} \\ \\ \\ we \: have \: to \: take \\ \\ cot \theta \: - tan \theta \: = \frac{cos \theta}{sin \theta} - \frac{sin \theta}{cos \theta} \\ \\ \\ so \: \\ cot \theta - tan \theta = 2cot2 \theta \\ \\ \\ \\ tan \theta = \: cot \theta \: - 2cot2 \theta \\ \\ tan \frac{ \pi}{16} + 2tan \frac{ \pi}{8} + 4 \\ \\ = cot \frac{ \pi}{16} - 2cot \frac{ \pi}{8} + 2 \bigg(cot \frac{ \pi}{8} - 2cot \frac{ \pi}{4} \bigg) + 4 \\ \\ = cot \frac{ \pi}{8} - 4cot \frac{ \pi}{4} + 4 \\ \\ = cot \frac{ \pi}{16} \\ \\ proved$