If A, B, C be the angles of a triangle, then A + B A + B = - Vidyadip

MCQ

If $A, B, C$ be the angles of a triangle, then $\sum {\frac{{\cot A + \cot B}}{{\tan A + \tan B}} = } $

✓
$1$
B
$2$
C
$-1$
D
$-2$

✓

Answer

Correct option: A.

$1$

a
(a) $ = \sum\limits_{}^{} {\frac{{\sin B\cos A + \sin A\cos B}}{{\sin A.\sin B}}} \frac{{\cos A.\cos B}}{{(\sin A\cos B + \cos A.\sin B)}}$
$ = \sum\limits_{}^{} {\cot A\cot B} $
As we know if $A + B + C = \pi $, then
$\cot A\cot B + \cot B\cot C + \cot C\cot A = 1$.

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