What is the general solution for sin(x)-2cos(x)sin(x)=0 ?

The general solution for sin(x)-2cos(x)sin(x)=0 is x=2pin,x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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

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

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Factor

sin (x) - 2 cos (x) sin (x) : - sin (x) (2 cos (x) - 1)

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) - 1 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

\frac{3}{5} = cos (x)

tan (θ) = \frac{36}{20 + 16}

tan (h) = \frac{9}{9 3}

arcsin (x) + arcsin (3 x) = \frac{π}{2}

cos (x) sin (x) = \frac{1}{2}

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