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

2 cos^2(75)-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 2 cos^2(\theta)-1 where θ = 75 degrees and see where that gets us.

There is a trig identity that says

cos(2 \theta) = 2 cos^2(\theta) - 1

Using that, we can write your expression as

2 cos^2(75)-1 = cos(2 \, \cdot \, 75)

or

2 cos^2(75)-1 = cos(150)


That should do it.