Proving tan⁡(x+π3)=4tan⁡x+3sec2xsec2x−4tan2x

Arely Briggs

Arely Briggs

Answered

2022-01-23

Proving tan(x+π3)=4tanx+3sec2xsec2x4tan2x

Answer & Explanation

chaloideq1

chaloideq1

Expert

2022-01-24Added 11 answers

Let me start from what you already got:
tanx+313tanx
=(tanx+3)(1+3tanx)(13tanx)(1+3tanx)
=tanx+3tan2x+33tanx13tan2x
=4tanx+3sec2x3+343sec2x
=4tanx+3sec2x4(sec2xtan2x)3sec2x
=4tanx+3sec2xsec2x4tan2x

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