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If tan x + cot x = 2 ,Find the value of tan^2x + cot^2x
$tan x + cot x =2 \ (tanx + cot x)^2\ tan^2x +cot^2x +2tan xcdot cotx =4\ tan^2x +cot^2x + 2 =4 \tan^2x + cot^2x =2$
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$tan x + cot x =2 \ (tanx + cot x)^2\ tan^2x +cot^2x +2tan xcdot cotx =4\ tan^2x +cot^2x + 2 =4 \tan^2x + cot^2x =2$
? If tan x + cot x = 2 , find the value of tan^2 x + cot^2x

Solution: we have

$\tan x + cot x = 2 \ \ (tan x +cot x)^2 =4 \ \ tan^2x +cot^2 x + 2 tanx * cot x =4 \ \ tan^2x + cot^2x +2 =4\ \ tan^2x +cot^2x =2$

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