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

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

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

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

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

Solution steps

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

Switch sides

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{3 π}{2} + 2 πn

Combine all the solutions

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

6 tan^{2} (x) - 18 = 0

11 sin^{2} (θ) - 5 sin (θ) = 4

cos (\frac{π x}{4}) = \frac{1}{2}

x, cos (2 x) = 1

5 cos (x) cot (x) = 1

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