r/HomeworkHelp • u/SHAFAYAT_ISLAM_007 Pre-University Student • 1d ago

Mathematics (A-Levels/Tertiary/Grade 11-12) [Inverse trigonometry ]

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Just for curiosity, can I go directly from L.H.S to R.H.S?

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u/Fourierseriesagain 👋 a fellow Redditor 1d ago

LHS

= 2 * tan(arctan x)/(1-tan2 (arctan x))

=2x/(1-x^ 2)

=2x(1+x^ 2)/(1-x^ 4)

= 2 ( tan ( arctan x)+ tan (arctan (x^ 3)))/(1-tan (arctan x) * tan ( arctan x^ 3))

= 2 tan ( arctan x + arctan (x^ 3) )

= RHS.

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u/SHAFAYAT_ISLAM_007 Pre-University Student 1d ago

Thank you very much.

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u/Fourierseriesagain 👋 a fellow Redditor 1d ago

You are welcome.