Question

If $(2\cos 2A-1)(\tan 3A-1)=0$ and if one of the value of angle $A$ is ${30}^{\circ }$ find the other value of angle $A$.

Answer 1

Given, $(2\cos 2A-1)(\tan 3A-1)=0$

Either $2\cos 2A-1=0$ or $\tan 3A-1=0$

$\cos 2A=\frac{1}{2}$ or $\tan 3A=1$

$\cos 2A=\cos {60}^{\circ }$ or $\tan 3A=\tan {45}^{\circ }$

$2A={60}^{\circ }$ or $3A={45}^{\circ }$

$A={30}^{\circ }$ or $A={15}^{\circ }$
$A={30}^{\circ },{15}^{\circ }$

Hence, other value of angle $A$ is ${15}^{\circ }$.