Question

If $\sin \theta +\cos \theta =1$, then what is the value of $\sin \theta \cos \theta$?

• A. $2$
• B. $0$
• C. $1$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$0$

Given, $\sin \theta +\cos \theta =1$

Squaring both sides gives,
${\sin }^2\theta +{\cos }^2\theta +2\sin \theta \cos \theta =1$
$\Rightarrow 1+2\sin \theta \cos \theta =1$
$\Rightarrow 2\sin \theta \cos \theta =0$
$\Rightarrow \sin \theta \cos \theta =0$