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°

`= tan(90^@ - 70^@) tan(90^@ - 55^@) tan 45^@ tan 55^@ tan 70^@`

`= cot 70^@ cot 55^@ tan 45^@ tan 55^@ tan 70^@`

`= (tan 70^@ cot 70^@)(tan 55^@ cot 55^@) tan  45`

= 1 x 1 x 1

= 1

Proved