it is a projectile motion based , i think a tough question , not getting answer even by several attempt

The range of the projectile motion is given by

R=u²sin2?/g

Time of flight is given by

T=2usin?/g

 

Let d? be the fractional change in the value of the angle.

 

Differentiating R w.r.t ? we get

dR/d? = 2u²cos2?/g

Multiply by d? on both sides, we get

dR= 2u²cos2?d?/g

This represents the change in range, so fractional change in range would be to divide this change with the original value of range.

Fractional change in Range = dR/R = 2cos2?d?/sin2? =x

 

Now, 

Differentiating T w.r.t ? we get

dT/d? = 2ucos?/g

Multiply by d? on both sides, we get

dR= 2ucos?d?/g

This represents the change in time of flight, so fractional change in time of flight would be to divide this change with the original value of time of flight.

Fractional change in Time of flight = dT/T = cos?d?/sin? =y

 

So, x= 2cos2?d?/sin2?  and y= cos?d?/sin?

And ?=60, putting the value of ? we get

x=2(cos120)d?/sin120 = -2d?/?3

y=cos60d?/sin60 = d?/?3 = -x/2 is the answer