Question

Find the distance between (a cosa,a Sina) and (-a Sina, a cosa).​

Answer 1

Answer:

$\large\boxed{\sf{\sqrt{2}a\;\;units}}$

Step-by-step explanation:

Given points are

(a cos a, a sin a) and (-a sin a, a cos a)

By distance formula

The distance between them is equal to

$= \sqrt{ {( a \cos a + a \sin a) }^{2} + {(a \sin a - a \cos a)}^{2} } \\ \\ = \sqrt{ {a}^{2} ( { \cos }^{2}a + { \sin }^{2}a + 2 \sin a \cos a) + {a}^{2} ( { \sin }^{2}a + { \cos }^{2} a - 2 \sin a \cos a) } \\ \\ = \sqrt{ { a }^{2} (1 + \sin 2a) + {a}^{2}(1 - \sin2a) } \\ \\ = \sqrt{ {a}^{2}(1 + \sin2a + 1 - \sin2a ) } \\ \\ = \sqrt{ {a}^{2}(1 + 1) } \\ \\ = \sqrt{2 {a}^{2} } \\ \\ = \sqrt{2} a$

Hence, distance between points is √2a units

Answer 2

Step-by-step explanation:

the answer is √2*a units

simply substitute in the distance formula and simplify.

Hope it helped.....