If tan A=2tanB+cotB, then 2tan(A-B)=

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Question

If tan A=2tanB+cotB, then 2tan(A-B)=

Options:

A . tanB

B . 2tanB

C . cotB

D . 2cotB

Answer: Option C
:
C

2 tan(A - B) = 2 $(\frac{t a n A - t a n B}{1 + t a n A t a n B})$

= 2
$\frac{(2 t a n B + c o t B - t a n B)}{1 + (2 t a n B + c o t B) t a n B}$ = 2
$\frac{t a n B + c o t B}{2 (1 + t a n^{2} B)}$

=
$\frac{c o t B (t a n^{2} B + 1)}{(1 + t a n^{2} B)}$ = cot B.

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