Best Answer:
The horizontal range is

R = u cos θ * T where T is the time of flight.

T = 2 u sin θ / g

Hence

R = u^2 * 2 sin θ cos θ / g

R = [u^2/g] sin 2θ

Since [u^2/g] is a constant, R depends only upon the value of sin 2θ

We know that the minimum value of sin 2θ is zero and the maximum value of sin 2θ is 1.

If 2θ varies from zero to 90 degree, sin 2θ varies from zero to 1.

If θ = 45°, 2 θ = 90° and sin 2 θ = sin 90 = 1.

If θ is changed from zero to 45°, R attains the maximum value of [u^2/g] at 45°,

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{For values more and less than 45, R is less than this value of [u^2/g].

For example if θ = 15, sin 2*15 = sin 30 = 0.5. The range is half the maximum value.

if θ = 75 sin 2*75 = sin 150 = 0.5. The range is again half the maximum value.

Hence for angles more and above 45 by equal amounts, the range is the same but is less than the maximum value of 45 degree}.

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