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

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

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

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

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

Solution steps

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

Rewrite using trig identities

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

Factor

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

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

Solving each part separately

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

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

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

sin (x) tan (x) - 6 tan (x) = 0

tan (θ) = sin (θ)

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

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

sin (9 x) = - \frac{3}{2}

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