Find ALL exact radian solutions to the equation: sinx + 2sinxcosx = 0?

sinx + 2 sinx cosx = 0
sinx (1 + 2 cosx) = 0
sinx = 0  or  1 + 2 cosx = 0
sinx = 0  or  cosx = -1/2
x = nπ  or  x = 2nπ ± (2π/3)  where n = 0, 1, 2 …..

For 0 ≤ x ≤ 2π
x = 0, 2π/3, π, 4π/3, 2π

sin x + 2 sin x * cos x  =  0

=> sin x ( 1 + 2 cos x )  =  0

=> sin x = 0  and cos x =  - (1/2)

Mark that sin x = +ve and cos x = -ve, Hence x must lie in SECOND quadrant .

=> x = nπ or x = 2nπ + (2π/3) where n = 0, 1, 2 ….. , 

=> x  =  0,  (2π/3) , ....... Radians.

Factor out sinx then solve for each factor.