If tan A + cot A = 2, where 0 < A < 90°, then what is the value of tan2 A + tan3 A + tan4 A + .... + tann A?

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CDS Elementary Mathematics 3 Sep 2023 Official Paper
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  1. 1
  2. n - 2
  3. n - 1
  4. n

Answer (Detailed Solution Below)

Option 3 : n - 1
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Detailed Solution

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Given:

If tan A + cot A = 2

Concept used: 

tan 45° = 1

Calculation:

Putting A = 45° 

tan 45°  + cot 45°  = 2 

So, tan 45° = 1

Thus, given condition is satisfied. 

According to the question,

tan2A + tan3A + tan4A + .....+ tann

⇒ 1 + 1 + 1 + .... (n - 1)times

∴  tan2 A + tan3 A + tan4 A + .... + tann A =  n-1

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