Use the substitution method and then factor
Let u=sinx
so, u^2=sin^2x
2color(red)(u^2)-5color(red)(u)+2=0
Now you can factor
Multiply the coefficient of the first term, 2, with the last term, 2.
2*2=4
Ask yourself what are the factors of 4 that add up to the coefficient of the middle term, -5?
Factors of 4
(1)(4) => NO
color(red)((-1)(-4)) => color(red)(YES)
(2)(2) => NO
(-2)(-2) => NO
Now place those factors in an order that makes it easy to factor by grouping.
(2u^2color(red)(-4u))+(color(red)(-1u)+2)=0
Factor out 2u from the first grouping.
Factor out -1 from the second grouping.
color(red)(2u)(u-2)color(red)(-1)(u-2)=0
Now you can factor out a grouping, (u-2)
(u-2)(2u-1)=0
Now use the Zero Property
u-2=0 and 2u-1=0
u=2 and u=1/2
Now switch back to sinx
sin x=2 and sin x =1/2
cancel(sin x=2) is discarded because sin x oscillates between -1 and 1.
Falling back to trigonometry sin x is in the ratio y/r
y/r=1/2 which means that x=sqrt3 by using the pythagorean theorem x=sqrt(2^2-1^2)=sqrt(4-1)=sqrt3 or knowing that we have the special triangle , 30,60,90 which corresponds to the sides 1,sqrt3,2.
The side of length 1 corresponds to 30 degrees which is also pi/6
All of that to say that
sin (pi/6)=1/2
x={pi/6}
I have tutorials on methods of factoring found here, https://www.youtube.com/playlist?list=PLsX0tNIJwRTxqIIcfpsTII9_xhqVIbQlp
