Question

the distance between the points ( cos Q, sin Q) AND (sin Q,cos Q)

Answer 1

Distance between two points is positive Square Root of sum of Square of difference of ordinates and absiccas .

So distance between two points D = √{ (sinθ - cos θ)² +(cos θ+ sinθ)²}

D = √[ (sinθ )² + (cos θ)² - 2 sin θ cosθ +(cos θ )² + ( sin θ) ² +2 cos θ sinθ) ]

Since (sinθ )² + (cos θ)² = 1

Therefore

D= √[ ( 1 - 2 sin θ cosθ + 1 +2 cos θ sinθ) ]

Cancelling 2 sin θ cos θ and -2 cos θ sinθ)

D = √2

is the required answer

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