Question

If $\tan \theta =\cot \theta$ find value of $\sin \theta +\cos \theta$

Answer 1

Given, $\tan \theta =\cot \theta$

$\tan \theta =\frac{1}{\tan \theta }\Rightarrow {\tan }^2\theta =1$

$\tan \theta =\pm 1$

$\therefore \theta =\pm \pi /4$

$\sin \theta +\cos \theta \Rightarrow \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\sqrt{2}$

$1/\sqrt{2}-1\sqrt{2}=0$