Find all values of x in the interval 0 2 that satisfy the gi

Find all values of x in the interval [0, 2] that satisfy the given equation. (Enter your answers as a comma-separated list.)

Solution

sin2x = -sqrt2*sinx

we know sin2x = 2sinxcosx

so, 2sinxcosx = -sqrt2 *sinx

2sinxcosx +sqrt2 *sinx =0

sinx( 2cosx +sqrt2) =0

sinx =0 ----> x=0, pi , 2pi

2cosx +sqrt2 =0

cosx = -sqrt2/2

x= pi-pi/4 , pi+pi/4 = 3pi/4, 5pi/4

Solution :in the interval [0, 2] x= 0,pi , 3pi/4 , 5pi/4 , 2pi