If $A + B + C = π$ and $cos A = cos B cos C$ then value of $tan A$ in terms of B and C is

tan B tan C

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tan B + tan C

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tan B - tan C

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tan C - tan B

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Solution

The correct option is C $tan B + tan C$
Given $A + B + C = π$ and $c o s A = c o s B c o s C$
$\Rightarrow c o s (π - (B + C)) = c o s B c o s C$
$- c o s (B + C) = c o s B c o s C$
$- c o s B c o s C + s i n B s i n C = c o s B c o s C$
$s i n B s i n C = 2 c o s B c o s C$
$t a n B t a n C = 2$ - 1
$t a n π = 0 \Rightarrow t a n (A + B + C) = 0$
$\Rightarrow t a n A + t a n B + t a n C = t a n A t a n B t a n C$
$t a n A + t a n B + t a n C = 2 t a n A$
$\Rightarrow t a n A = t a n B + t a n C$
$[t a n (A + B + C) = \frac{t a n A + t a n B + t a n C - t a n A t a n B t a n C}{(1 - t a n A t a n B - t a n B t a n C - t a n C t a n A)}]$

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