Yes, what you did is the way to go.

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- November 23rd 2012, 04:41 PM #1
## sec^2(x)=4tan(x)

Hello

The question is solve on the interval

using the identity

I get:

I can't factor that, so I completed the square and got.

It looks like that will give me the solutions, but I've never completed the square on a trigonometric function before and just wanted to check that it's the right way to proceed.

Thank you.

- November 23rd 2012, 04:46 PM #2

- November 23rd 2012, 04:57 PM #3

- November 23rd 2012, 06:55 PM #4
## Re: sec^2(x)=4tan(x)

If you are solving for x there is another useful identity: the double angle formula.

As long as we agree that cos(x) is not zero we may cancel one of the cosine terms:

Now, 2 sin(x) cos(x) = sin(2x). Thus

And go from there. I get that

- November 23rd 2012, 07:53 PM #5

- November 23rd 2012, 10:15 PM #6

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- November 23rd 2012, 10:25 PM #7

- November 24th 2012, 07:39 AM #8