Write the expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression

I got it to 2 cos2 (45+30) -1 usingthe addition and subraction formula but I'm lost from there

2 cos2(75degrees) - 1

What is the original question?

the original question was Write the expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression

What was the expression? Surely it's wasn't "2 cos2 (45+30) -1", was it?

No it was 2 cos2(75 degrees) - 1

I don't get it. You can actually solve that. There's no need for a closed form solution. OK. Enough rant...

Let's look at where θ = 75 degrees and see where that gets us.

There is a trig identity that says



Using that, we can write your expression as



or




That should do it.