Question

If $2\sin A\cos A-\cos A-2\sin A+1=0$, then one value of A is ${30}^{\circ }$. The other value is:

Answer 1

$2sinAcosA-cosA-2sinA+1=0$
$2\sin A(\cos A-1)-1(\cos A+-1)=0$
$(2\sin A-1)(\cos A-1)=0$
$\sin A=\frac{1}{2}$ or $\cos A=1$
$\sin A=\sin 30$ or $\cos A=\cos 0$
$A={30}^{\circ }$ or $A=0^{\circ }$
Thus, $A=0^{\circ },{30}^{\circ }$