Question

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Answer 1

Solution :

Let us assume two points P and Q such that

P - ( a cos theta , a sin theta )

Q - ( a cos phi , a sin phi )

PQ = 2a units.

( PQ )² = 4 a²

=> ( a cos theta - a cos phi )² + ( a sin theta - a sin phi )²

=> a² [ cos theta - cos phi ]² + a² [ sin theta - sin phi ]²

=> a² { [ cos theta - cos phi ]² + [ sin theta - sin phi ]² } = 4 a²

=> [ cos theta - cos phi ]² + [ sin theta - sin phi ]² = 4

=> cos² theta + cos ² phi - 2 cos theta cos phi + sin² theta + sin² phi - 2 sin theta sin phi = 4

=> { cos² theta + sin ² theta } + { cos² phi + sin ² phi } - 2{ cos theta cos phi + sin theta sin phi } = 4

We know that sin ² A + cos² A = 1

So,

- 2{ cos theta cos phi + sin theta sin phi } = 2

=> { cos theta cos phi + sin theta sin phi = -1

=> cos ( phi - theta ) = -1 { Cos a - b formula }

=> phi - theta = cos ^-1 ( -1)

theta = phi - cos inverse of -1 .

This is the required answer .

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