Radian Find all values of x in the Interval [0,2Pi] that satisfy the equation

[Hancko]

Dear Tutors, I please request help with the following question 69:




Here are my workings for question 69:

 

[skeeter]

[MATH]\sin(2x) = \cos{x}[/MATH]
[MATH]2\sin{x}\cos{x} - \cos{x} = 0[/MATH]
[MATH]\cos{x}(2\sin{x}-1) = 0[/MATH]
[MATH]\cos{x} = 0 \implies x \in \left\{ \frac{\pi}{2},\frac{3\pi}{2} \right\}[/MATH]
[MATH]\sin{x} = \frac{1}{2} \implies x \in \left\{ \frac{\pi}{6},\frac{5\pi}{6} \right\}[/MATH]

 

[Hancko]

T

[MATH]\sin(2x) = \cos{x}[/MATH]
[MATH]2\sin{x}\cos{x} - \cos{x} = 0[/MATH]
[MATH]\cos{x}(2\sin{x}-1) = 0[/MATH]
[MATH]\cos{x} = 0 \implies x \in \left\{ \frac{\pi}{2},\frac{3\pi}{2} \right\}[/MATH]
[MATH]\sin{x} = \frac{1}{2} \implies x \in \left\{ \frac{\pi}{6},\frac{5\pi}{6} \right\}[/MATH]

Thank you.

 

[nasi112]

That was brilliant skeeter.