An equation containing sine and cosine

[BlueStreak]

Solve for x; give solutions within the interval [0, 2π)
3 sinx = 1 + cos2x

 

[Otis]

Hello. What have you tried or thought about, so far?

Hint: We can get an equation in quadratic form, by using a double-angle identity for cos(2x).

?

 

[BlueStreak]

@Otis Would I convert cos(2x) to cos²x-sin²x?

 

[Harry_the_cat]

That wouldn't help much. Use the identity that involves sin only.

 

[BlueStreak]

@Harry_the_cat @Otis Thank you so much! I figured it out. My answers were π/6 and 5π/6. Appreciate the help! ?