what is the distance between (cosO,0)and(0,sinO)
Answers
Answer: root 2
Step-by-step explanation: If the x-y axes are perpendicular, the (shortest) distance d between two points A and B having co-ordinates (x₁, y₁) and (x₂, y₂) respectively in Euclidean plane is given by the formula
d = +√[(x₁ - x₂)² + (y₁ - y₂)²] …………………………………………………..(1)
Given, A = (sin θ - cos θ, 0) and B = (0, sin θ + cos θ)
∴ x₁ = sin θ - cos θ, y₁ = 0
and x₂ = 0, y₂ = sin θ + cos θ
Substituting these values of x₁, x₂ and y₁, y₂ in equation (1),
d = √[( sin θ - cos θ - 0)² + (0 - sin θ - cos θ)²]
= √[( sin θ - cos θ)² + (-1)²(sin θ + cos θ)²]
= √[( sin θ - cos θ)² + (sin θ + cos θ)²]
= √( sin² θ - 2sin θ cos θ + cos² θ + sin² θ + 2sin θ cos θ + cos² θ)
= √[( sin² θ + cos² θ) + (sin² θ + cos² θ)] (Cancelling the term 2sin θ cos θ)
= √( 1 + 1) = √2
Hence the distance between the points A=(sin θ-cos θ,0) & B=(0, sin θ+cos θ)
= √2 (Answer)
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