Question

Without using trigonometric tables, prove that:

tan48° tan23° tan42° tan67° = 1

Answer 1

LHS = tan 48° tan23° tan42° tan67°

= cost (90° - 48°) cost (90° - 23°) tan 42° tan 67°

= cot 42° cot 67° tan 42° tan 67°

`= 1/(tan 42°)xx1/(tan 67°)xxtan 42° xx tan 67°`

= 1 

= RHS