Very simple expand 8 cot8A = 4(cot4A - tan4A)
Hence 4tan4A will be cancelled
4cot4A = 2(Cot2A - Tan2A)
Therefore 2Tan2A will be cancelled .
Then 2Cot2A = Cot A -TanA .
Tan A is cancelled left is Cot A
Prove: cot A - tan A = 2 cot 2A
Hence prove
tan A+2tan2A+4tan4A+8 Cot 8A =Cot A
Very simple expand 8 cot8A = 4(cot4A - tan4A)
Hence 4tan4A will be cancelled
4cot4A = 2(Cot2A - Tan2A)
Therefore 2Tan2A will be cancelled .
Then 2Cot2A = Cot A -TanA .
Tan A is cancelled left is Cot A