If tanx + cotx =5 tgen find tan^2x +cot^2x

(tanx+cotx)^2 = 5^2

tan^2x + 2 + cot^2x = 25
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To find tan^2x + cot^2x, we need to manipulate the given equation tanx + cotx = 5 first.

1. Start by squaring both sides of the equation:
(tanx + cotx)^2 = 5^2
tan^2x + 2tanxcotx + cot^2x = 25

2. Next, we need to simplify the middle term 2tanxcotx using the identity:
tanxcotx = 1
The equation becomes:
tan^2x + 2(1) + cot^2x = 25
tan^2x + 2 + cot^2x = 25

3. Rearrange the terms:
tan^2x + cot^2x = 25 - 2
tan^2x + cot^2x = 23

Therefore, tan^2x + cot^2x = 23.