Question

If $sin\theta +cos\theta =1,$ then $\left(sin\theta cos\theta \right)$ is equal to

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

Answer 1

The correct option is A $0$

$\sin \theta +\cos \theta =1{\left(\sin \theta +\cos \theta \right)}^2=1^2{\sin }^2\theta +{\cos }^2\theta +2\sin \theta .\cos \theta =11+2\sin \theta .\cos \theta =1\sin \theta .\cos \theta =0$