Solving tan⁡2x=1+2sin⁡4x

Kathy Williams

Kathy Williams

Answered

2022-01-15

Solving tan2x=1+2sin4x

Answer & Explanation

Travis Hicks

Travis Hicks

Expert

2022-01-16Added 29 answers

By tangent half angle identities we have that by t=tan(2x)
tan2x=1+2sin4xt=1+4t1+t2t3t23t1=0
(t+1)(t22t1)=0
Tiefdruckot

Tiefdruckot

Expert

2022-01-17Added 46 answers

Hint:
sin2x=cos2x(1+2sin4x)=cos2x+sin6x+sin2x
using Werner Formulas
cos2x=sin6x=cos(π2+6x)
as cos(π2+y)=siny
2x=2mπ±(π2+6x)
+ x=(4m+1)π8
- x=(4m1)π16

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