Question

Show that: $\tan {35}^{\circ }\tan {60}^{\circ }\tan {55}^{\circ }\tan {30}^{\circ }=1$

Answer 1

To show: $\tan {35}^{\circ }\tan {60}^{\circ }\tan {55}^{\circ }\tan {30}^{\circ }=1$

We have,

$\tan {35}^{\circ }=\tan ({90}^{\circ }-{55}^{\circ })=\cot {55}^{\circ }$
and $\tan {60}^{\circ }=\tan ({90}^{\circ }-{30}^{\circ })=\cot {30}^{\circ }$

$\therefore \tan {35}^{\circ }\tan {60}^{\circ }\tan {55}^{\circ }\tan {30}^{\circ }$

$=\cot {55}^{\circ }\cot {30}^{\circ }\tan {55}^{\circ }\tan {30}^{\circ }$

$=\frac{1}{\tan {55}^{\circ }}\times \frac{1}{\tan {30}^{\circ }}\times \tan {55}^{\circ }\times \tan {30}^{\circ }$

$=1$

Hence, the required value is $1$ .