2sin^2 x= sqrt2 sin x

Question

Solve

 

Answer 1

2sin²x - √2sinx = 0

 

sinx(2sinx - √2) = 0

 

sinx = 0 or sinx = √2/2

 

Solutions between 0° and 360° (inclusive):

 

   sinx = 0 when x = 0°, 180°, 360°

 

   sinx = √2/2 when x = 45°, 135°

 

Answer 2

2sin^2x=√2sinx

sin^2x=(√2/2)sinx

sin^2x/sinx=√2/2

sinx=√2/2

draw a diagram to see that x=45º or look on the unit circle

x=135º also (sine is positive in the second quadrant also)