The distance between the points (a cos α ,a sin α ) and a cos β ,a sin β is

Question

Tardigrade Admin · Accepted Answer

Points (a cos α ,a sin α ) and (a cos β ,a sin β ) , distance between the points =√(a cos α -a cos β )2+(a sin α -a sin β )2 =√ beginalign a2( cos 2α + cos 2β + sin 2α + sin 2β -2 cos α . cos β +2 sin α . sin β ) endalign =|a|√ beginalign ( sin 2α + cos 2α )+( sin 2β + cos 2β ) -2( cos α . cos β + sin α . sin β ) endalign =|a|√2-2 cos (α -β ) =|a|√2√1- cos (α -β ) =√2|a|√2 sin 2((α -β )/2) =|a| √2 √2 | sin ((α -β )/2) | =2| a. sin ((α -β )/2) |

Q. The distance between the points $(a cos α, a sin α)$ and $a cos β, a sin β$ is

$2 ∣ ∣ sin (\frac{α - β}{2}) ∣ ∣$

$2 ∣ ∣ a sin (\frac{α - β}{2}) ∣ ∣$

$2 ∣ ∣ a cos (\frac{α - β}{2}) ∣ ∣$

$∣ ∣ a cos (\frac{α - β}{2}) ∣ ∣$

$2∣ a (1 - cos (α - β)) ∣$

Q. The distance between the points (acosα,asinα) and acosβ,asinβ is

2∣∣​sin(2α−β​)∣∣​

2∣∣​asin(2α−β​)∣∣​

2∣∣​acos(2α−β​)∣∣​

∣∣​acos(2α−β​)∣∣​