Question

These are numeric entry type questions.
If $\frac{\cos 18^{\circ}+\sin 18^{\circ}}{\cos 18^{\circ}-\sin 18^{\circ}}=\tan A$, then $A=$____

Answer 1

$ \frac{\cos 18^{\circ}+\sin 18^{\circ}}{\cos 18^{\circ}-\sin 18^{\circ}}=\tan A $
$ \frac{\cos (63-45)+\sin (63-45)}{\cos (63-45)-\sin (63-45)}=\tan A $
$ = \frac{\cos 63 \cos 45+\sin 63 \sin 45+\sin 63 \cos 45-\cos 63 \sin 45}{\cos 63 \cos 45+\sin 63 \sin 45-\sin 63 \cos 45+\cos 63 \sin 45} $
$ = \frac{\frac{\cos 63}{\sqrt{2}}+\frac{\sin 63}{\sqrt{2}}+\frac{\sin 63}{\sqrt{2}}-\frac{\cos 63}{\sqrt{2}}}{\sqrt{2}}+\frac{\sin 63}{\sqrt{2}}-\frac{\sin 63}{\sqrt{2}}+\frac{\cos 63}{\sqrt{2}} $
$ = \frac{2 /}{\sqrt{2}} \sin 63 $
$ \frac{2}{\sqrt{2}} \cos 63 $
$ \Rightarrow A=63^{\circ}$