Could somebody please help me with this one identities problem?

[sillyrascal]

This question looks like it should be super easy but I’ve been scratching my head at it for an embarrassingly long time. I might just be sleep deprived (or stupid) but it won’t work for me. We’re supposed to “solve each equation for x in the interval [0, 2π).” I’ve learned about the half-angle formula and the substitution method but I’m not really getting anywhere. If somebody could help me out, I would really appreciate it.

 

[Deleted member 4993]

This question looks like it should be super easy but I’ve been scratching my head at it for an embarrassingly long time. I might just be sleep deprived (or stupid) but it won’t work for me. We’re supposed to “solve each equation for x in the interval [0, 2π).” I’ve learned about the half-angle formula and the substitution method but I’m not really getting anywhere. If somebody could help me out, I would really appreciate it.

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Please share your work/thoughts about this problem.

Think how you could factorize the denominator.

 

[Harry_the_cat]

Think of cos (x) as cos( 2 * x/2).

 

[BigBeachBanana]

This question looks like it should be super easy but I’ve been scratching my head at it for an embarrassingly long time. I might just be sleep deprived (or stupid) but it won’t work for me. We’re supposed to “solve each equation for x in the interval [0, 2π).” I’ve learned about the half-angle formula and the substitution method but I’m not really getting anywhere. If somebody could help me out, I would really appreciate it.

I would use double-angle for [imath]\cos(x)[/imath] to simplify the left-hand side. That would give you a quadratic to work with.
[math]\cos(x)=\cos(2\cdot\frac{x}{2})[/math]

 

[Harry_the_cat]

I would use double-angle for [imath]\cos(x)[/imath] to simplify the left-hand side. That would give you a quadratic to work with.
[math]\cos(x)=\cos(2\cdot\frac{x}{2})[/math]

Snap!