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Question

Accepted Answer

Given tan A + cot A = 2 and A is acute.

Step 1: Use the identity tan A + cot A = (tan^2 A + 1) / tan A.

Let tan A = t.
Then tan A + cot A = t + 1/t = 2.

Multiply both sides by t:
 t^2 + 1 = 2t

Rearranged:
 t^2 - 2t + 1 = 0

This is (t - 1)^2 = 0

So, t = tan A = 1.

Step 2: Calculate each term:
- tan^8 A = 1^8 = 1
- cot A = 1 / tan A = 1 / 1 = 1
- cot^8 A = 1^8 = 1
- sec^2 A = 1 + tan^2 A = 1 + 1 = 2

Step 3: Substitute values into the expression:
7tan^8 A - 6cot^8 A + 8sec^2 A = 7*1 - 6*1 + 8*2 = 7 - 6 + 16 = 17

Therefore, the value is 17.

Answer

Answer

Answer