Question

it's very very urgent Plss solve this question

Answer 1

the distance between points (-acos @ , bsin @) ( asin @ , - bcos @ )



d = √ ( asin @ + acos @ )^2 + (-bcos @ - bsin @)^2

d = √ (a)^2 ( 1+sin 2@) + (b)^2 ( 1+sin 2@)

d = √ (1+sin 2@) (a^2 + b^2)

Answer 2

Distance between the points :

$( - a \cos \alpha, b \sin\alpha ) \: and \: (a \sin \alpha ,- b \cos\alpha )$

Now,

$\sqrt{[ ({a \sin \alpha ) - ( - a \cos\alpha})]^{2} + {( - b \cos\alpha - b \sin\alpha })^{2} } \\ \\ = > \sqrt{ {a}^{2} {( \sin \alpha + \cos\alpha) }^{2} + {b}^{2} {( \sin\alpha + \cos \alpha) }^{2} } \\ \\ = > \sqrt{( {a}^{2} + {b}^{2} ) {( \sin\alpha + \cos \alpha) }^{2} } \\ \\ = > \sqrt{( {a}^{2} + {b}^{2} )( { \sin}^{2} \alpha + { \cos}^{2} \alpha + 2 \sin \alpha \cos\alpha ) } \\ \\ = > \sqrt{( {a}^{2} + {b}^{2} )(1 + \sin2\alpha) }$