Question

2sin^2(x)+sin(2x)=2

please help!!

Answer 1

`2sin {}^(2) (x) + sin(2x) = 2 \\ 2sin {}^(2) (x) + 2sin(x)cos(x) = 2 \\ sin {}^(2) (x) + sin(x)cos(x) - 1 = 0 \\1 - cos {}^(2) (x) + sin(x)cos(x) - 1 = 0 \\ - cos {}^(2) (x) + sin(x)cos(x) = 0`

`cos(x)( - cos(x) + sin(x)) = 0`

`cos(x) = 0 \\ x = (\pi)/(2) + k\pi \\ \\ sin(x) = cos(x) \\ x = (\pi)/(4) + k\pi`