Math CentralQuandaries & Queries


Question from tony, a student:

list all real solutions of the equation that are in the interval [0,2π)

2cos(x) + tan(x) = sec(x)

Hi Tony.

First convert this to sine and cosine:

Then multiply by cos(x):

Now use the identity sin2 (x) + cos2 (x) = 1 to change it all to a single trig function:

And this is just a quadratic in sin(x). So you can use the quadratic formula if you wish, or try to factor it.

Can you finish the problem now?
Penny and Stephen La Rocque.

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