Verified answer

= sin⁴(θ) - cos⁴(θ)

= [sin²(θ)]² - [cos²(θ)]² → you recognize: a² - b² = (a + b).(a - b)

= [sin²(θ) + cos²(θ)].[sin²(θ) - cos²(θ)] → recall: sin²(θ) + cos²(θ) = 1

= sin²(θ) - cos²(θ)

...

Sen^4 θ - Cos^4 θ = Sen^2 θ - Cos^2 θ

(Sen^2 θ - Cos^2 θ)(Sen^2 θ + Cos^2 θ =

(Sen θ - Cos θ)(Sen θ + Cos θ)

(Sen θ - Cos θ)(Sen θ + Cos θ)(Sen^2 θ + Cos^2 θ) =

(Sen θ - Cos θ)(Sen θ + Cos θ)

Sen^2 θ + Cos^2 θ = 1

1 = 1

Suerte

Hola

Recordamos la igualdad pitagórica

Sen^2(θ) + Cos^2(θ) = 1

Recordamos la diferencia de cuadrados

(Sen^2(θ) + Cos^2(θ)) (Sen^2(θ) - Cos^2(θ)) =

= (Sen^2(θ))^2 - (Cos^2(θ) )^2

Nos queda

1 * (Sen^2(θ) - Cos^2(θ)) =

= Sen^4(θ) - Cos^4(θ)

Sen^4(θ) - Cos^4(θ) = Sen^2(θ) - Cos^2(θ)