Prove that the horizontal range id same when angle of projection is (i) greater than ` 45^(@)` by certain value and (ii) less than ` 45^(@)` by the same value.

Explanation

Horizontal range for angular projection of a projectile is given by
` R=( u^2 sin 2 theta)/g`
Case (i) When angle of projection, ` theta 45^@+ alpha`,
let ` R _1 (say) , then
` R_1 = (u^2 sin 2 (45^@ - alpha)/g = u^2/g sin (90^@ + 2 alpha)`
`= (u^2 cos 2 alpha )/g ` ....(i)
Case (ii) When angle of projection, ` theta =45^@ -alpha` ,
leta, ` R= R_2 (say), then
`R_2 = (u^2 sin (45^@ -alpha)/g`
`= u^2/g sin (90^@ - 2 alpha) = u^2/g cos 2 alpha ` ...(i)
From equation (i) and (ii) , ` R_2 =R_2 `.