Question

If $\sin \theta +\cos \theta =1$, then $\sin \theta \cos \theta$ equal to :

• A. $0$
• B. $\frac{1}{\sqrt{3}-1}$
• C. $1$
• D. $\frac{1+\sqrt{2}}{1+\sqrt{3}}$

Answer 1

Answer: (A)

$0$

Let $\sin \theta +\cos \theta =1$
Squaring both side, we get
${\sin }^2\theta +{\cos }^2\theta +2\sin \theta \cos \theta =1$
$\Rightarrow \sin \theta \cos \theta =0$
Hence, option 'A' is correct.