Mathematics - Trigonometric Equation Question with Solution | TestHub

$\sin A=\sin B\Rightarrow \sin A-\sin B=0$

$\Rightarrow 2\sin \frac{\mathrm{A}-\mathrm{B}}{2}\cos \frac{\mathrm{A}+\mathrm{B}}{2}=0$

and $\cos \mathrm{A}=\cos \mathrm{B}\Rightarrow \cos \mathrm{B}-\mathrm{Cos}\mathrm{A}=0$

$\Rightarrow 2\sin \frac{\mathrm{A}+\mathrm{B}}{2}\sin \frac{\mathrm{A}-\mathrm{B}}{2}=0$

Equations (1) and (2) are simultaneously true if $\sin (1/2)(A-B)=0$,

while the other factors $\sin (1/2)(A+B)$ and

$\cos (1/2)(A+B)$ cannot both be zero simultaneously.