Question

two projectile are projected at angles pie/4+theta and pie/4-theta with the horizontal where theta is greater than pie/4 with same speed the ratio of horizontal range described by them is​

Answer 1

I assume that you mean θ < π/4

Range of a projectile R = u²sin(2θ)/g

sin($\frac{\pi}{2}$-2θ) = cos(2θ)

sin($\frac{\pi}{2}$+2θ) = cos(2θ)

for angle of projection $\frac{\pi}{4}$ - θ

sin(2 ($\frac{\pi}{4}$-θ)) = cos(2θ)

for angle of projection $\frac{\pi}{4}$ + θ

sin(2 ($\frac{\pi}{4}$+θ)) = cos(2θ)

By careful observation you'll see that both the ranges are same for angles of projection ($\frac{\pi}{4}$-θ) and ($\frac{\pi}{4}$+θ)

Hence ratio of ranges is 1:1