JEE Advance - Mathematics (1998 - No. 29)
Prove that $$\tan \,\alpha + 2\tan 2\alpha + 4\tan 4\alpha + 8\cot 8\alpha = \cot \alpha $$
The given equation is incorrect.
Use the identity $\cot x - \tan x = 2\cot 2x$ repeatedly.
Use the identity $\tan x - \cot x = 2\cot 2x$ repeatedly.
Use the identity $\tan x + \cot x = 2\csc 2x$ repeatedly.
Use the identity $\tan x - \cot x = -2\cot 2x$ repeatedly.