Write the value of $\tan 10^{\circ} \tan 15^{\circ} \tan 75^{\circ} \tan 80^{\circ} ?$
We have to find: $\tan 10^{\circ} \tan 15^{\circ} \tan 75^{\circ} \tan 80^{\circ}$
$=\tan 10^{\circ} \tan 15^{\circ} \tan 75^{\circ} \tan 80^{\circ}$
$=\tan \left(90^{\circ}-80^{\circ}\right) \tan \left(90^{\circ}-75^{\circ}\right) \tan 75^{\circ} \tan 80^{\circ}$ $\left[\tan \left(90^{\circ}-\theta\right)=\cot \theta\right]$
$=\cot 80^{\circ} \cot 75^{\circ} \tan 75^{\circ} \tan 80^{\circ}$
$=\left(\cot 75^{\circ} \tan 75^{\circ}\right)\left(\cot 80^{\circ} \tan 80^{\circ}\right)$
$=1 \times 1$
$=1$$[\cot \theta \cdot \tan \theta=1]$
Hence the value of $\tan 10^{\circ} \tan 15^{\circ} \tan 75^{\circ} \tan 80^{\circ}$ is 1
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.