Question

Cot a - tan a = 2 cot 2a?

Answer 1

$$\begin{gathered} \mathrm{LHS}=\cot \mathrm{a}-\tan \mathrm{a} \\ =\frac{\cos \mathrm{a}}{\sin \mathrm{a}}-\frac{\sin \mathrm{a}}{\cos \mathrm{a}} \\ =\frac{{\cos }^2\mathrm{a}-{\sin }^2\mathrm{a}}{\sin \mathrm{a}.\cos \mathrm{a}} \\ =\frac{\cos 2\mathrm{a}}{\sin \mathrm{a}.\cos \mathrm{a}} \\ =\frac{2\cos 2\mathrm{a}}{2\sin \mathrm{a}.\cos \mathrm{a}} \\ =\frac{2\cos 2\mathrm{a}}{\sin 2\mathrm{a}} \\ =2\cot 2\mathrm{a} \\ =\mathrm{RHS} \end{gathered}$$