Proving tan2(π4+x)=1+sin⁡(2x)1−sin⁡(2x)

Haialarmz6

Haialarmz6

Answered

2022-01-26

Proving tan2(π4+x)=1+sin(2x)1sin(2x)

Answer & Explanation

fionaluvsyou0x

fionaluvsyou0x

Expert

2022-01-27Added 11 answers

tan2(π4+x)
=(tanπ4+tanx1tanπ4tanx)2
=(1+tanx)2(1tanx)2
=(1+sinxcosx)2(1sinxcosx)2
=(cosx+sinx)2(cosxsinx)2
=sin2x+cos2x+2sinxcosxsin2x+cos2x2sinxcosx
=1+2sinxcosx12sinxcosx
=1+sin2x1sin2x
sphwngzt

sphwngzt

Expert

2022-01-28Added 11 answers

1±sin2x=(cosx±sinx)2
cosx+sinxcosx+sinx=1+tanx1tanx=tan(x+π4)

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