Question
Download Solution PDFIf tan A + cot A = 2, where 0 < A < 90°, then what is the value of tan2 A + tan3 A + tan4 A + .... + tann A?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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 + .....+ tannA
⇒ 1 + 1 + 1 + .... (n - 1)times
∴ tan2 A + tan3 A + tan4 A + .... + tann A = n-1
Last updated on May 29, 2025
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