Question : If $\tan \theta -\cot \theta =0$, find the value of $\sin \theta +\cos \theta$.
Option 1: $0$
Option 2: $1$
Option 3: $\sqrt{2}$
Option 4: $2$
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Correct Answer: $\sqrt{2}$
Solution :
Given:
$\tan\theta -\cot\theta =0$
$⇒\tan\theta=\cot\theta$
$\therefore\theta = 45^{\circ}$
$\therefore \sin\theta +\cos\theta = \sin45^{\circ} + \cos45^{\circ}=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\frac{2}{\sqrt2}=\sqrt2$
Hence, the correct answer is $\sqrt2$.
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