2sin^2x cosx = 1, solving a quadratic trig function

In this problem we need to use the Pythagorean identity to rewrite sin^2(x) in terms of cosine and then factor and solve. There are three distinct families of curves. I find all solutions and then generate the solutions on the domain [0,2pi)

[@josev8226]

how would you work out this problem if both both sin and cos were squared. 2sin^2(x)cos^2(x)

[@MathBySarah]

Jose V, if it is equal to 1 I would set it equal to zero and factor into (sqrt(2)sin(x)cos(x) - 1)(sqrt(2)sin(x)cos(x) + 1)=0. And then each factor could be set to zero. And you can use the double angle identity to convert the sin(x)cos(x) into something easier to work with.

[@valed3028]

Gracias 😁

[@rovsaneli561]

Niece