Question

$\frac{\tan {80}^0-\tan {10}^0}{\tan {70}^0}$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is C $2$

$\frac{\tan {80}^0-\tan {10}^0}{\tan {70}^0}$

We know that,

$\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}$

$\therefore \tan {80}^0-\tan {10}^0$

$=\tan ({80}^0-{10}^0)(1+\tan {80}^0\tan {10}^0)$

$=\tan {70}^0(1+\tan {80}^0\tan {10}^0)$

Then, $\frac{\tan {80}^0-\tan {10}^0}{\tan {70}^0}$

$=\frac{\tan \left({70}^0\right)(1+\tan {80}^0\tan {10}^0)}{\tan {70}^0}$

$=(1+\tan {80}^0\tan {10}^0)$

$=1+\cot ({90}^0-{80}^0)\tan {10}^0$

$=1+\cot \left({10}^0\right)\tan {10}^0$

$=1+1$

$=2$