Verified answer

Note that sin(2x) = 2sin(x)cos(x). Then...

2sin(x)cos(x) - cos(x) = 0

cos(x)(2sin(x) - 1) = 0

Hence, by zero-product property, we have...

cos(x) = 0 and 2sin(x) - 1 = 0

x = ±π/2 + 2πk

. . . π/6 + 2πk

. . . 5π/6 + 2πk where k is the integer

You determine the answers by yourself

I hope this helps!

sin(2x)=2sin(x)cos(x) so

sin(2x)=cos(x) can be rewritten

2sin(x)cos(x)=cos(x)

2sin(x)cos(x)-cos(x)=0 factor cos(x)[2sin(x)-1]=0

cos(x)=0 gives pi/2 (90) and 3pi/2 (270) and 2sin(x)-1=0 so sin(x)=1/2 giving pi/6 (30) and 5pi/6 (150)