Solving 2n·cos²(n)=1000

[dirtyaldante]

Homework Statement

Solve for n:

2n.Cos^2(n)=1000

The Attempt at a Solution

So, I think there's a substitution involved here. I tried to rearrange cosine in terms of sine to make it into a quadratic but that didn't work. I've gone through all the table trig identities. I've had other ideas but it's all come to bubkiss. Wolfram equation solver spat out a solution for n but that's not really the point...

Can anybody shed any light on this?

 

[Mentallic]

If can't be solved in terms of elementary functions. Your best bet is to find a numerical solution, so either take Wolfram's word for it or solve it using some approximation technique such as halving the interval or Newton's method.