tanA +2tan2A+4tan4A+8cot8Acot A\ttan A\tcos A\tsin Aplease answer with the solution

If tan A + 2*tan 2A + 4*tan 4A + 8*cot 8A = cot A ,

hi,

we can solve it as  follow

= tan A + 2*tan 2A + 4*tan 4A + 8*cot 8A - cot A = 0

now  tan A + cot A = 2*cosec 2A & cot A - tan A = 2*cot 2A

so,we proceed using these equations.

tan A + 2*tan 2A + 4*tan 4A + 8*cot 8A - cot A

= tan A - cot A + 2*tan 2A + 4*tan 4A + 8*cot 8A

= – 2*cot 2A + 2*tan 2A + 4*tan 4A + 8*cot 8A

= – 2*2*cot 4A + 4*tan 4A + 8*cot 8A

= – 4*2*cot 8A + 8*cot 8A

= 0 .hence proved