Question

If $\tan A-2\cos A\tan A+2\cos A-1=0$ and one value of A is ${45}^{\circ }$, the other value is:

Answer 1

$\tan A-2\cos A\tan A+2\cos A-1=0$
$\tan A(1-2\cos A)-1(1-2\cos A)=0$
$(\tan A-1)(1-2\cos A)=0$

$\tan A=1$ or $\cos A=\frac{1}{2}$
$\tan A=\tan {45}^o$ or $\cos A=\cos {60}^o$
$A={45}^{\circ },{60}^{\circ }$

Therefore,

Other Value of $A={60}^o$