Question

Show that:
$\tan {10}^o\tan {15}^o\tan {75}^o\tan {80}^o=1$

Answer 1

$\to$ As ${\tan }^{\circ }(90-\theta )=\cot \theta$

$\Rightarrow \tan 10=tan(90-80)=\cot 80$

and $tan15=\tan (90-75)=\cot 75$

$\Rightarrow \tan 10\tan 15\tan 75\tan 80$

$=\cot 80\cot 75\tan 75\tan 80$

As $\tan \theta =\frac{1}{cot\theta }\Rightarrow \tan \theta \cot \theta =1$

$\Rightarrow$ Quantity $=1$