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

The general solution for cos(x/2)2-sin(x)=0 is x=pi+4pin,x=3pi+4pin

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

cos (\frac{x}{2}) 2 - sin (x) = 0

x = π + 4 πn, x = 3 π + 4 πn

Solution steps

cos (\frac{x}{2}) \cdot 2 - sin (x) = 0

Let:

u = \frac{x}{2}

cos (u) \cdot 2 - sin (2 u) = 0

Rewrite using trig identities

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

Factor

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

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

Solving each part separately

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

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

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

Combine all the solutions

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

Substitute back

u = \frac{x}{2}

\frac{x}{2} = \frac{π}{2} + 2 πn : x = π + 4 πn

\frac{x}{2} = \frac{3 π}{2} + 2 πn : x = 3 π + 4 πn

x = π + 4 πn, x = 3 π + 4 πn

a, cos (a x) + (\frac{b}{x}) sin (a x) = 0

x, csc (2 x) = \frac{1}{2} (sec (θ)) (cos (θ))

sin (θ) = \frac{3 2 - 3}{40}

cos^{2} (x) + 5 cos (x) - 3 = 0

2 sin^{2} (x) - sin (x) cos (x) - cos^{2} (x) = 0

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