Question -
Answer -
Given f (x) = cos2 x
⇒ 
⇒ f’(x)= 2 cos x (–sin x)
⇒ f’(x)= –2 sin (x) cos (x)
⇒ f’(x)= –sin2x
Now, as given x belongs to (0, π/2).
⇒ 2x ∈ (0, π)
⇒ Sin(2x)> 0
⇒ –Sin(2x) < 0
⇒ f’(x)< 0
Hence, condition for f(x) to be decreasing
Thus f(x) is decreasing on interval (0, π/2).
Hence proved