Question

If $\sin A=\sin B$ and $\cos A=\cos B$, then $\sin \frac{A-B}{2}=$

Answer 1

We have $\sin A=\sin B$ and $\cos A=\cos B$
or $\sin A-\sin B=0$ and $\cos A-\cos B=0$
or $2\sin \left(\frac{A-B}{2}\right)\cos \left(\frac{A+B}{2}\right)=0$ and $-2\sin \left(\frac{A-B}{2}\right)\sin \left(\frac{A+B}{2}\right)=0$
or $\sin \frac{A-B}{2}=0$, which is common for both the equation.
Ans :0