If 69^ + 66^ - 69^ 66^ =2k, then k = - Vidyadip

MCQ

If $\tan69^\circ+\tan66^\circ-\tan69^\circ\tan66^\circ=2\text{k},$ then $k =$

A
$-1$
B
$\frac12$
✓
$\frac{-1}{2}$
D
none of these

✓

Answer

Correct option: C.

$\frac{-1}{2}$

$\tan135^\circ=\tan(90^\circ+45^\circ)$
$=-\tan45^\circ$
$=-1$
Or, $\tan(69^\circ+66^\circ)=\frac{\tan69^\circ+\tan66^\circ}{1-\tan69^\circ\tan66^\circ}$
$\Rightarrow-1=\frac{\tan69^\circ+\tan66^\circ}{1-\tan69^\circ\tan66^\circ}$
$\Rightarrow\tan69^\circ+\tan66^\circ-\tan69^\circ+\tan66^\circ=-1$
$\therefore2\text{k}=-1$
$\Rightarrow\text{k}=\frac{-1}{2}$

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