Do बिंदुओं (0,cos)and (sin,0) ke मध्य ki duri

Mathematics

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दो बिंदुओं (x1,y1)(x_1, y_1) और (x2,y2)(x_2, y_2) के बीच की दूरी का सूत्र है:

D=(x2−x1)2+(y2−y1)2D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

यहां दिए गए बिंदु हैं:
(x1,y1)=(0,cos⁡θ)(x_1, y_1) = (0, \cos \theta)
(x2,y2)=(sin⁡θ,0)(x_2, y_2) = (\sin \theta, 0)

  1. दूरी सूत्र में मान प्रतिस्थापित करें

    D=(sin⁡θ−0)2+(0−cos⁡θ)2D = \sqrt{(\sin \theta - 0)^2 + (0 - \cos \theta)^2}

  2. पदों को सरल करें

    D=(sin⁡θ)2+(−cos⁡θ)2D = \sqrt{(\sin \theta)^2 + (-\cos \theta)^2} D=sin⁡2θ+cos⁡2θD = \sqrt{\sin^2 \theta + \cos^2 \theta}

  3. त्रिकोणमितीय सर्वसमिका का प्रयोग करें

    हम जानते हैं कि sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1

    D=1D = \sqrt{1}

  4. वर्गमूल ज्ञात करें

    D=1D = 1

    अतः, दो बिंदुओं के बीच की दूरी है:

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