बिंदुओं (a cos θ, 0) तथा (0, a sin θ) के बीच की दूरी होगी 

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Bihar STET TGT (Maths) Official Paper-I (Held On: 04 Sept, 2023 Shift 2)
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  1. a
  2. a cos θ 
  3. a sin θ 
  4. 1

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Option 1 : a
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अवधारणा -

2D तल में दो बिंदुओं \((x_1, y_1)\) तथा \((x_2, y_2)\) के बीच की दूरी, दूरी के सूत्र का उपयोग करके ज्ञात की जा सकती है:

\(\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

स्पष्टीकरण -

इस मामले में, बिंदु हैं (a cos θ, 0) और (0, a sin θ) इसलिए, दूरी के सूत्र को लागू करने पर:

\(\begin{align*} \text{Distance} &= \sqrt{ (0 - a \cos \theta)^2 + (a \sin \theta - 0)^2 } \\ &= \sqrt{a^2 \cos^2 \theta + a^2 \sin^2 \theta} \\ &= \sqrt{a^2 (\cos^2 \theta + \sin^2 \theta)} \\ &= \sqrt{a^2} \\ &= |a| \end{align*}\)

इस प्रकार, बिंदुओं (a cos θ, 0) और (0, a siθ) के बीच की दूरी |a| है।

अतः विकल्प (1) सत्य है।

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