Simplify `(2sin2A-sin4A)/(2sin2A+sin4A)`  Please explain it. Thanks!

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thilina-g | College Teacher | (Level 1) Educator

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`(2sin2A - sin4A)/(2sin2A+sin4A)`

`= (2sin2A - 2sin2Acos2A)/(2sin2A+2sin2Acos2A)`

Dividing both numerator and denominator by `2sin2A`

`= (1-cos2A)/(1+cos2A)`

I can write `cos2A` as,

`cos2A = 1-2sin^2A`

and

`cos2A = 2cos^2A-1`

`= (1-(1-2sin^2A))/(1+(2cos^2A-1))`

`= (2sin^2A)/(2cos^2A)`

`= tan^2A`

 

Therefore,

`(2sin2A - sin4A)/(2sin2A+sin4A) = tan^2A`

 

 

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