Question

Prove that  tan 20° tan 35° tan 45° tan 55° tan 70° = 1

Answer 1

We are asked to find the value of tan 20° tan 35° tan 45° tan 55° tan 70°

${\displaystyle =\tan ({90}^{\circ }-{70}^{\circ })\tan ({90}^{\circ }-{55}^{\circ }){\tan 45}^{\circ }{\tan 55}^{\circ }{\tan 70}^{\circ }}$

${\displaystyle ={\cot 70}^{\circ }{\cot 55}^{\circ }{\tan 45}^{\circ }{\tan 55}^{\circ }{\tan 70}^{\circ }}$

${\displaystyle =\left({\tan 70}^{\circ }{\cot 70}^{\circ }\right)\left({\tan 55}^{\circ }{\cot 55}^{\circ }\right)\tan 45}$

= 1 x 1 x 1

= 1

Proved