Question

If tan A, tan B , tanC are in arithmetic progression then cotA, cotB ,cot C are in ?? ​

Answer 1

Answer:

Harmonic progression

Step-by-step explanation:

If tan A, tan B and tan C are in arithmetic progression, then cot A, cot B and cot C are in harmonic progression.

⇒ Harmonic progressions are progressions written by taking reciprocals of each term of an arithmetic progression.

⇒ Here, as cotangent is reciprocal of tangent, then,

• cot A = 1/tan A
• cot B = 1/tan B
• cot C = 1/tan C

⇒ The arithmetic progression is tan A, tan B, tan C,...

⇒ Thus the harmonic progression is,

• cot A, cot B, cot C,...
• 1/tan A, 1/tan B, 1/tan C,...

$\mapsto\ \cot A,\ \cot B,\ \cot C... \ \ \ =\ \ \ \frac{1}{\tan A},\ \frac{1}{\tan B},\ \frac{1}{\tan C},...$