Show by computing derivatives, that sin^2x=-1/2cos2x+c for some constant c. Find c by setting x=0?

I'm a little lost on how to approach this problem. Any help would be appreciated, thanks guys

Show by computing derivatives, that sin^2x=-1/2cos2x+c for some constant c. Find c by setting x=0?
Define function f(x)= sin^2(x)+ 1/2*cos(2x)


Compute its derivative


f'(x)=2sin(x)*cos(x) - 1/2*2*sin(2x) by the Power Rule/Chain Rule


Simplify f'(x) using trig identity sin(2x)=2sin(x)cos(x)


You get f'(x)=0


So f(x)=c for some constant c.





Since f(x) is constant it has the same value c for any x.


So f(0)=sin^2(x)+ 1/2*cos(0) =1/2 = c

crab apple