Let f(x)= sin x cos x

But we know sin2x=2sin x cos x

Applying the first derivative we get

Applying the derivative,

⇒ f’(x)=cos2x……(i)

Putting f’(x)=0,we get critical points as

cos2x=0

Now equating the angles, we get

Now we will find out the second derivative by deriving equation (i), we get

Applying the derivative,

⇒ f’’ (x)=-sin 2x.2

⇒ f’’(x)=-2sin2x

Now we will find the value of f’’(x) at , we get

But , so above equation becomes

Therefore at , f(x) is maximum and is the point of maxima.

Now we will find the maximum value of sin x cos x by substituting , in f(x), we get

f(x)= sin x cos x

Hence the maximum value of sin x cos x is

So the correct option is option B.