Can anyone me with these two problems?

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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