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

The general solution for sin(2x)=cos(x/2) is No Solution for x\in\mathbb{R}

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

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

No Solution for x \in R

Solution steps

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

Rewrite using trig identities

sin (2 x) = sin (\frac{π}{2} - \frac{x}{2})

Apply trig inverse properties

2 x = \frac{π}{2} - \frac{x}{2} + 2 πn, 2 x = π - (\frac{π}{2} - \frac{x}{2}) + 2 πn

2 x = \frac{π}{2} - \frac{x}{2} + 2 πn : x = \frac{π + 4 πn}{5}

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

Since the equation is undefined for:

\frac{π + 4 πn}{5}, \frac{π + 4 πn}{3}

No Solution for x \in R

5 - 7 sin (x) - 2 cos^{2} (x) = 0

2 + cos (θ) = 0

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

cos (3 x) - cos (5 x) = 0

2 = 2 cos (x)

What is the general solution for sin(2x)=cos(x/2) ?
The general solution for sin(2x)=cos(x/2) is No Solution for x\in\mathbb{R}