Question

prove: TanA+2Tan2A+4Tan4A+8Cot8A=CotA​

Answer 1

Step-by-step explanation:

Consider: Cot A - Tan A - 2 Tan 2 A

We know Cot A - Tan A

= cos²-sin²A / cin A. cos A = 2 cot 2 A

= 2 cot 2 A - 2 Tan 2 A

= 2 (cot 2 A - tan 2 A)

=2 (2cot 4 A)

4 cot 4 A

Similarly: Cot A - tan A - 2 Tan A - 4 tan 4 A

= 4 cot 4 A - 4 tan 4 A

= 4 (cot 4 A - tan 4 A)

= 8 cot 8 A

i.e, cot A - tan A - 2tan A - 4 tan 4 A = 8 cot 8 A

So, Tan A + 2 Tan A + 4 Tan 4 A + 8 Cot 8 A = Cot A

Answer is Cot A.