Use Bolzanos's theorem (at least there is a root in the interval) and prove that is strictly decreasing (only one root).
Prove sinx+cosx=x has a single solution in [0,pi/2]
This question seems very strange to me. How can I prove there is a single solution for every number between 0 and pi/2?
I'm not sure what formula to use.
I'm learning infinitesimal math.
Can someone help me out?
In the given domain,
The 2nd derivative of is negative, so it is concave downward for the given domain.
The maximum value of occurs when
The straight line line cuts the sinusoidal curve
somewhere in the given domain
and since is concave downward in the domain,
which is relevant after the maximum value of
then only one intersection occurs.