Number of extreme values of  f(x) = sin x + cos2x in (0, 2π ) is

f(x)=sinx+cosx  in (0,2π)                 f1(x)=0⇒cosx−sin2x.2=0                 ⇒cosx−4sinxcosx=0                 ⇒cosx(1−4sinx)=0                 ⇒cosx[1−4sinx]=0                 ⇒cosx=0,sinx=14                 ⇒x=π2,3π2⇒x∈I,II                 ∴f(x) has four extreme values