Question : If $\tan \theta-\cot \theta=4$, then find the value of $\tan ^2 \theta+\cot ^2 \theta$.
Option 1: 16
Option 2: 20
Option 3: 14
Option 4: 18
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Correct Answer: 18
Solution :
$\tan \theta-\cot \theta=4$
Squaring both sides,
⇒ $\tan^2\theta + \cot^2\theta - 2\tan\theta \cot\theta = 16$
⇒ $\tan^2\theta + \cot^2\theta = 16+2$
$\therefore \tan^2\theta + \cot^2\theta = 18$
Hence, the correct answer is 18.
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