sin70° - sin50° -cos80° = কত?

আমরা জানি,

$\sin A-\sin B=2 \cos \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)$

এখন, $A=70^{\circ}$ এবং $B=50^{\circ}$, তাই:

$\begin{array}{c} \sin 70^{\circ}-\sin 50^{\circ}=2 \cos \left(\frac{70^{\circ}+50^{\circ}}{2}\right) \sin \left(\frac{70^{\circ}-50^{\circ}}{2}\right) \\ =2 \cos \left(\frac{120^{\circ}}{2}\right) \sin \left(\frac{20^{\circ}}{2}\right) \\ =2 \cos 60^{\circ} \sin 10^{\circ} \\ =2 \times \frac{1}{2} \times \sin 10^{\circ} \\ =\sin 10^{\circ} \end{array}$

আমরা জনি,

$\cos 80^{\circ}=\sin 10^{\circ}$

$\sin 70^{\circ}-\sin 50^{\circ}-\cos 80^{\circ}=\sin 10^{\circ}-\sin 10^{\circ}=0$