Question

tan 20° x tan 40° x tan 80° = tan 60°​

Answer 1

Answer:Given, tan 20 * tan 40 * tan 80

= tan 40 * tan 80 * tan 20

= [{sin 40 * sin 80}/{cos 40 * cos 80}] *(sin 20/cos 20)

= [{2 * sin 40 * sin 80}/{2 * cos 40 * cos 80}] *(sin 20/cos 20)

= [{cos 40 - cos 120}/{cos 120 + cos 40}] *(sin 20/cos 20)

= [{cos 40 - cos (90 + 30)}/{cos (90 + 30) + cos 40}] *(sin 20/cos 20)

= [{cos 40 + sin30}/{-sin30 + cos 40}] *(sin 20/cos 20)

= [{(2 * cos 40 + 1)/2}/{(-1 + cos 40)/2}] *(sin 20/cos 20)

= [{2 * cos 40 + 1}/{-1 + cos 40}] *(sin 20/cos 20)

= [{2 * cos 40 * sin 20 + sin 20}/{-cos 20 + cos 40 * cos 20}]

= (sin 60 - sin 20 + sin 20)/(-cos 20 + cos 60 + cos 20)

= sin 60/cos 60

= tan 60

So, tan 20 * tan 40 * tan 80 = tan 60

Step-by-step explanation: