What is the general solution for 2sin(x)cos(x)+sqrt(2)sin(x)=0,0<= x<2pi ?

The general solution for 2sin(x)cos(x)+sqrt(2)sin(x)=0,0<= x<2pi is x=0,x=pi,x=(3pi)/4 ,x=(5pi)/4

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2sin(x)cos(x)+sqrt(2)sin(x)=0,0<= x<2pi

2 sin (x) cos (x) + 2 sin (x) = 0, 0 \leq x < 2 π

x = 0, x = π, x = \frac{3 π}{4}, x = \frac{5 π}{4}

Solution steps

2 sin (x) cos (x) + 2 sin (x) = 0, 0 \leq x < 2 π

Factor

2 sin (x) cos (x) + 2 sin (x) : sin (x) (2 cos (x) + 2)

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

Solving each part separately

sin (x) = 0 or 2 cos (x) + 2 = 0

sin (x) = 0, 0 \leq x < 2 π : x = 0, x = π

2 cos (x) + 2 = 0, 0 \leq x < 2 π : x = \frac{3 π}{4}, x = \frac{5 π}{4}

Combine all the solutions

x = 0, x = π, x = \frac{3 π}{4}, x = \frac{5 π}{4}

(cos (x) + 1) = 0

cos (x) = - 1, sin (x)

3 cos (2 θ) - 5 cos (θ) = 1

sin (2 x) = 4 cos (2 x)

- 9 cos^{2} (θ) + 1 = sin (θ)

What is the general solution for 2sin(x)cos(x)+sqrt(2)sin(x)=0,0<= x<2pi ?
The general solution for 2sin(x)cos(x)+sqrt(2)sin(x)=0,0<= x<2pi is x=0,x=pi,x=(3pi)/4 ,x=(5pi)/4