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| 1. |
Tan 20 ta40 tan 8o is equal to tan 60 prove |
| 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... | |