What is the general solution for sin(2x)=cos(8x) ?

The general solution for sin(2x)=cos(8x) is No Solution for x\in\mathbb{R}

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sin(2x)=cos(8x)

sin (2 x) = cos (8 x)

No Solution for x \in R

Solution steps

sin (2 x) = cos (8 x)

Rewrite using trig identities

sin (2 x) = sin (\frac{π}{2} - 8 x)

Apply trig inverse properties

2 x = \frac{π}{2} - 8 x + 2 πn, 2 x = π - (\frac{π}{2} - 8 x) + 2 πn

2 x = \frac{π}{2} - 8 x + 2 πn : x = \frac{π + 4 πn}{20}

2 x = π - (\frac{π}{2} - 8 x) + 2 πn : x = - \frac{π + 4 πn}{12}

Since the equation is undefined for:

\frac{π + 4 πn}{20}, - \frac{π + 4 πn}{12}

No Solution for x \in R

8 = sin (x)

arctan (4 x) + arctan (6 x) = - \frac{π}{2}

- 2 cot (x) + csc^{2} (x) = 0

sin (3 x + \frac{π}{4}) = \frac{3}{2}

\frac{cos ( x ) - sin ( x )}{cos ( x )} = tan (x) - 1

What is the general solution for sin(2x)=cos(8x) ?
The general solution for sin(2x)=cos(8x) is No Solution for x\in\mathbb{R}