Q66 / 160 · AP EAMCET 2007 · Mathematics

$\frac{\tan 80^{\circ}-\tan 10^{\circ}}{\tan 70^{\circ}}$ is equal to

  • A
    $0$
  • B
    $1$
  • Correct answer
    C
    $2$
  • D
    $3$

Solution

Now, $\frac{\tan 80^{\circ}-\tan 10^{\circ}}{\tan 70^{\circ}}$ $\begin{aligned} & =\frac{\tan 80^{\circ}-\tan 10^{\circ}}{\tan \left(80^{\circ}-10^{\circ}\right)} \\ & =\frac{\tan 80^{\circ}-\tan 10^{\circ}}{\tan 80^{\circ}-\tan 10^{\circ}} \times\left(1+\tan 80^{\circ} \tan 10^{\circ}\right) \\ & =1+\tan 80^{\circ} \tan 10^{\circ} \\ & =2\end{aligned}$

Hence, the correct answer is option: 'C'.

Relevant Questions