I'm having a hard time thinking of a way to solve this problem. How could I start?
Use the intermediate Value theorem to show that the equation cosx=x has at leat one solution.
The IVT says simply if f(x) is continuous on a closed interval [a,b] then
f(x) takes on every value between f(a) and f(b) at least once.
f(x) =cos(x) - x
f(0) = 1 > 0
f(pi) = -1-pi < 0
Therfore f(x) =cos(x) - x has a zero 0n [0,pi]
i.e there is an x st cos(x)- x = 0
or cos(x) = x