Galileo , inhis book Two new sciences , stated that for elevations which exceed or fall short of 45^(@) by equal amounts , the ranges are equal . Prove this statement.

Galileo , inhis book Two new sciences , stated that for elevations whi

1.	Galileo , inhis book Two new sciences , stated that for elevations which exceed or fall short of 45^(@) by equal amounts , the ranges are equal . Prove this statement.
Answer» <html><body><p></p>Solution :For a projectilelaunched with velocity `v_(@)` at an angle `theta_(@)` , therange is given by<br/>`R=(v_(0)^(2)sin2theta_(0))/(g)`<br/>Now , for angles , `(45^(@)+alpha)and(45^(@)-alpha),2theta_(0)` is`(<a href="https://interviewquestions.tuteehub.com/tag/90-341351" style="font-weight:bold;" target="_blank" title="Click to know more about 90">90</a>^(@)+2alpha)and(90^(@)-2alpha)`, respectively . The valuesof `sin(90^(@)+2alpha)andsin(90^(@)-2alpha)` are the same , <a href="https://interviewquestions.tuteehub.com/tag/equal-446400" style="font-weight:bold;" target="_blank" title="Click to know more about EQUAL">EQUAL</a> to that of `cos2alpha`. <a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a> , <a href="https://interviewquestions.tuteehub.com/tag/ranges-1177066" style="font-weight:bold;" target="_blank" title="Click to know more about RANGES">RANGES</a> are equal for elevations which exceed of fall short of `45^(@)` by equal amounts `alpha`.</body></html>