What is the general solution for sin(4x)=cos(x/2) ?

The general solution for sin(4x)=cos(x/2) is No Solution for x\in\mathbb{R}

Popular >

sin(4x)=cos(x/2)

sin (4 x) = cos (\frac{x}{2})

No Solution for x \in R

Solution steps

sin (4 x) = cos (\frac{x}{2})

Rewrite using trig identities

sin (4 x) = sin (\frac{π}{2} - \frac{x}{2})

Apply trig inverse properties

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

4 x = \frac{π}{2} - \frac{x}{2} + 2 πn : x = \frac{π + 4 πn}{9}

4 x = π - (\frac{π}{2} - \frac{x}{2}) + 2 πn : x = \frac{π + 4 πn}{7}

Since the equation is undefined for:

\frac{π + 4 πn}{9}, \frac{π + 4 πn}{7}

No Solution for x \in R

a, cos (a - b) = 2

cos (\frac{π}{2} - x) tan (x) - sec (- x) = 1

\frac{cot ( θ ) + csc ( θ )}{sec ( θ ) + 1} = sin (θ)

2 = cos^{2} (x)

(tan (x) - 1) (sin (x) - 1) = 0

What is the general solution for sin(4x)=cos(x/2) ?
The general solution for sin(4x)=cos(x/2) is No Solution for x\in\mathbb{R}