Question

Let $\theta$ being acute and $\sin \theta +\cos \theta =\sqrt{2}$. Then the value of $\tan \theta =$

• A. $0$
• B. $1$
• C. $-1$
• D. none of these

Answer 1

The correct option is B $1$

Given,

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

or, $\frac{1}{\sqrt{2}}.\sin x+\frac{1}{\sqrt{2}}.\cos x=1$

or, $\cos \frac{\pi }{4}.\sin x+\sin \frac{\pi }{4}.\cos x=1$

or, $\sin (x+\frac{\pi }{4})=\sin \frac{\pi }{2}$

or, $x=\frac{\pi }{4}$ [ Since $x$ is acute]

Now

$\tan \frac{\pi }{4}$

$=1$.