Math, asked by harshitsadhwani, 1 year ago

prove that tan20tan40tan80=tan60

Answers

Answered by amisha221

9

tan40.tan20.tan80 = tan60

Taking L.H.S.

tan40.tan80.tan20

=(sin40 sin80)sin20/cos40 cos80(cos20)

=(2sin40 sin80) sin20 / (2cos40 cos80)cos20

=(cos40- cos120) sin20 / (cos120 + cos40) cos20

=(2cos40 + 1)sin20 / (2cos40 - 1) cos20

=2cos40sin20 + sin20 / 2cos40cos20 - cos20

=sin60 - sin20 + sin20 / cos60 + cos20 - cos20

=sin60/cos60

=tan60 = R.H.S.

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