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Tan 20 ta40 tan 8o is …

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Tan 20 ta40 tan 8o is equal to tan 60 prove

Posted by Shalini Rajput 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Pihu Saini 6 years, 11 months ago

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...

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