Question

If sin $\theta +\cos \theta =\sqrt{2},$ and $\theta$ is acute, then $\tan \theta$ is equal to

• A. $\frac{1}{\sqrt{3}}$
• B. $1$
• C. $\sqrt{3}$
• D. $\infty$

Answer 1

The correct option is B $1$

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

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

or $\sin \theta \cos {45}^0+\cos \theta \sin {45}^0=1$

or $\sin (\theta +{45}^0)=\sin {90}^0$

or $\theta +{45}^0={90}^0$

or $\theta ={45}^0$

$\therefore \tan \theta =\tan {45}^0=1$