# If tanA + cotA = 2 . Find the value of tan^10A + cot^10A...............?

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- GlenguinLv 77 years agoFavorite Answer
This is a bit of a trick question; the answer is 2. First, remember that cotA = 1/tanA. Then let x = tanA. The equation becomes:

x + (1/x) = 2

which rearranges to

x² - 2x + 1 = 0

(x-1)² = 0,

so x = 1. Therefore tanA = cotA = 1, and A = 45°.

Since tan45° = cot45° = 1, then tan^10(45°) = cot^10 (45°) = 1^10 = 1 as well, and hence

tan^10A + cot^10A = 2.

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