Question

If $\sin x\cos x=\frac{1}{2}$, then what is the value of $\sin x-\cos x$

• A. $2$
• B. $1$
• C. $0$
• D. $-1$

Answer 1

The correct option is C $0$

• $2\left(\sin x\right)\left(\cos x\right)=1$ therefore $\sin \left(2x\right)=1$
  
• Hence $2x=90°$ therefore $x=45°$
• At $x=45°$ $\sin x=\cos x=\frac{1}{\sqrt{2}}$
• Therefore $\sin x-\cos x=0$