Question

Show that $\frac{\cos 9^o+\sin 9^o}{\cos 9^o-\sin 9^o}=\cot {36}^o$

Answer 1

Taking $LHS$

$\frac{\cos 9^{\circ }+\sin 9^{\circ }}{\cos 9^{\circ }-\sin 9^{\circ }}\frac{1+\tan 9^{\circ }}{1-\tan 9^{\circ }}\frac{\tan {45}^{\circ }+\tan 9^{\circ }}{1-\tan {45}^{\circ }\tan 9^{\circ }}\tan {(45}^{\circ }+9^{\circ })\tan {54}^{\circ }\cot (90^{\circ }-{54}^{\circ })\cot {36}^{\circ }$