Question

Without using trigonometric tables, prove that:
(i) tan 20° tan 40° tan 45º tan 50º tan 70° = 1​

Answer 1

Answer:

tan 45° = 1

tan 20° • tan 70° = tan20° • cot (90° - 70°)

= tan 20°•cot20° = 1

tan 40° • tan 50° = tan40° • cot (90° - 50°)

= tan 40°•cot40° = 1

tan20° tan40° tan45° tan50° tan70° = 1