Question about a trigonomic simplification that I can't wrap my head around

[Plecto]

An online calculator is able to simplify sqrt(2e^2t*sin²t+2e^2t*cos²​t) to sqrt(2)*e^t but I can't figure out how it's done. I've been messing about with the inverse euler's formula thinking that that might be the way to go, but I'm not getting anywhere. What kind of magic is this?

 

[Deleted member 4993]

An online calculator is able to simplify sqrt(2e^2t*sin²t+2e^2t*cos²​t) to sqrt(2)*e^t but I can't figure out how it's done. I've been messing about with the inverse euler's formula thinking that that might be the way to go, but I'm not getting anywhere. What kind of magic is this?

Hint:

2e^2t*sin²t+2e^2t*cos²​t = 2e^2t * (sin²t + cos²​t)

 

[Plecto]

Hint:

2e^2t*sin²t+2e^2t*cos²​t = 2e^2t * (sin²t + cos²​t)

sin²t+cos²t=1

sqrt(2e^2t*sin²t+2e^2t*cos²​t) = sqrt(2e^2t)Not quite there though

 

[Deleted member 4993]

sin²t+cos²t=1

sqrt(2e^2t*sin²t+2e^2t*cos²​t) = sqrt(2e^2t) = sqrt(2) * sqrt(e^2t)

Not quite there though

Are you just staring at the screen or working with paper&pencil??!!