If + = 2, then ^2 + ^2 = ? - Vidyadip

Question

If $\tan \theta + \cot \theta = 2$, then $\tan^2\theta + \cot^2\theta = ?$

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Answer

$tan θ + cot θ = 2 ....$[Given]
$\therefore (\tan \theta + \cot \theta )^2 = 4 ....$.[Squaring both sides]
$\therefore \tan^2\theta + 2tan \theta .\cot \theta + \cot^2\theta = 4 ......[\because (a + b)^2 = a^2 + 2ab + b^2]$
$\therefore \tan^2\theta + 2(1) + \cot^2\theta = 4 ......[\because \tan \theta ⋅ \cot \theta = 1]$
$\therefore \tan^2\theta + \cot^2\theta = 4 – 2$
$\therefore \tan^2\theta + \cot^2\theta = 2$

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