Question

If $\sin \theta +\cos \theta =\sqrt{2}$, then evaluate : $\tan \theta +\cot \theta$.

Answer 1

Given $\sin \theta +\cos \theta =\sqrt{2}$

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

$⟹\sin \theta \cos {45}^{\circ }+\cos \theta \sin {45}^{\circ }=\sin {90}^{\circ }$

$⟹\sin (\theta +{45}^{\circ })=\sin {90}^{\circ }$

$⟹{45}^{\circ }+\theta ={90}^{\circ }⟹\theta ={45}^{\circ }$

$\tan \theta +\cot \theta =\tan {45}^{\circ }+\cot {45}^{\circ }=1+1=2$