Question

If $\sin \theta +\cos \theta =1$, then $\sin \theta \cos \theta =$.

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

Answer 1

Answer: (A)

$0$

$\sin \theta +\cos \theta =1\Rightarrow {(\sin \theta +\cos \theta )}^2=1\Rightarrow {\sin }^2\theta +{\cos }^2\theta +2\sin \theta \cos \theta =1\Rightarrow 1+2\sin \theta \cos \theta =1\therefore \sin \theta \cos \theta =0$