Question

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

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

Answer 1

Answer: (B)

$1$

$\sin \theta +\cos \theta =\sqrt{2}$
$\Rightarrow {\sin }^2\theta +{\cos }^2\theta +2\sin \theta \cos \theta =2\Rightarrow 2\sin \theta \cos \theta =1$
$\Rightarrow \sin 2\theta =1\Rightarrow \frac{2{\tan }^2\theta }{1+{\tan }^2\theta }=1\Rightarrow {\tan }^2\theta =1\Rightarrow \tan \theta =\pm 1$
since $\theta$ is acute $\Rightarrow \tan \theta =1$