How to convert it into seconds?
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I don't like this computer aided instruction holding my hand. I'll ignore that at first so I can compare my solution to the one being taught.
We can see how a tan factors out; let's see what's left.
We need to factor out a sin x + cos x in the denominator so let's change one of the squared cosines to squared sine.
OK, now I can look at what they did.
First step ok, the box is 2 cos^2 x
Second step they changed the 1, box same as before: 2 cos^2 x
Third box matches our proof, cos^2 x
Fourth box our last box didn't change: cos^2 x
Fifth box: sin x + cos x