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Kos theeta barabar 2/3 tab 2g squire theeta plus 2 10 squire theeta mines nau ka man gyat kijiye math counting me sawal ko solve?
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Kos theeta barabar 2/3 tab 2g squire theeta plus 2 10 squire theeta mi...
समस्या का विवरण
आपके द्वारा दी गई समस्या में, हमें यह समीकरण हल करना है:
\[
\cos \theta = \frac{2}{3} \quad \text{और} \quad 2g \sin^2 \theta + 2 \cdot 10 \sin \theta = 0
\]
समीकरण को सुलझाना
1. पहले, \(\cos \theta\) के लिए \(\sin \theta\) का मान निकालें:
- ज्ञात है कि \(\sin^2 \theta + \cos^2 \theta = 1\) से:
\[
\sin^2 \theta = 1 - \cos^2 \theta = 1 - \left(\frac{2}{3}\right)^2 = 1 - \frac{4}{9} = \frac{5}{9}
\]
- इसका अर्थ है:
\[
\sin \theta = \frac{\sqrt{5}}{3} \quad \text{(सकारात्मक मान लेना)}
\]
समीकरण को सरल करना
2. अब, समीकरण \(2g \sin^2 \theta + 20 \sin \theta = 0\) में \(\sin \theta\) का मान डालें:
- \(\sin^2 \theta = \frac{5}{9}\) डालने पर:
\[
2g \left(\frac{5}{9}\right) + 20 \left(\frac{\sqrt{5}}{3}\right) = 0
\]
- इसे सरल बनाते हैं:
\[
\frac{10g}{9} + \frac{20\sqrt{5}}{3} = 0
\]
- इसे \(9\) से गुणा करने पर:
\[
10g + 60\sqrt{5} = 0
\]
ग का मान निकालना
3. यहाँ से \(g\) का मान निकाला जा सकता है:
\[
g = -6\sqrt{5}
\]
निष्कर्ष
इस प्रकार, \(g\) का मान \(-6\sqrt{5}\) है। यह समस्या गणितीय दृष्टिकोण से एक महत्वपूर्ण सवाल है जो त्रिकोणमिति और समीकरणों के ज्ञान को दर्शाता है।
आपके द्वारा दी गई समस्या में, हमें यह समीकरण हल करना है:
\[
\cos \theta = \frac{2}{3} \quad \text{और} \quad 2g \sin^2 \theta + 2 \cdot 10 \sin \theta = 0
\]
समीकरण को सुलझाना
1. पहले, \(\cos \theta\) के लिए \(\sin \theta\) का मान निकालें:
- ज्ञात है कि \(\sin^2 \theta + \cos^2 \theta = 1\) से:
\[
\sin^2 \theta = 1 - \cos^2 \theta = 1 - \left(\frac{2}{3}\right)^2 = 1 - \frac{4}{9} = \frac{5}{9}
\]
- इसका अर्थ है:
\[
\sin \theta = \frac{\sqrt{5}}{3} \quad \text{(सकारात्मक मान लेना)}
\]
समीकरण को सरल करना
2. अब, समीकरण \(2g \sin^2 \theta + 20 \sin \theta = 0\) में \(\sin \theta\) का मान डालें:
- \(\sin^2 \theta = \frac{5}{9}\) डालने पर:
\[
2g \left(\frac{5}{9}\right) + 20 \left(\frac{\sqrt{5}}{3}\right) = 0
\]
- इसे सरल बनाते हैं:
\[
\frac{10g}{9} + \frac{20\sqrt{5}}{3} = 0
\]
- इसे \(9\) से गुणा करने पर:
\[
10g + 60\sqrt{5} = 0
\]
ग का मान निकालना
3. यहाँ से \(g\) का मान निकाला जा सकता है:
\[
g = -6\sqrt{5}
\]
निष्कर्ष
इस प्रकार, \(g\) का मान \(-6\sqrt{5}\) है। यह समस्या गणितीय दृष्टिकोण से एक महत्वपूर्ण सवाल है जो त्रिकोणमिति और समीकरणों के ज्ञान को दर्शाता है।
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Kos theeta barabar 2/3 tab 2g squire theeta plus 2 10 squire theeta mines nau ka man gyat kijiye math counting me sawal ko solve?
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Kos theeta barabar 2/3 tab 2g squire theeta plus 2 10 squire theeta mines nau ka man gyat kijiye math counting me sawal ko solve? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Kos theeta barabar 2/3 tab 2g squire theeta plus 2 10 squire theeta mines nau ka man gyat kijiye math counting me sawal ko solve? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Kos theeta barabar 2/3 tab 2g squire theeta plus 2 10 squire theeta mines nau ka man gyat kijiye math counting me sawal ko solve?.
Kos theeta barabar 2/3 tab 2g squire theeta plus 2 10 squire theeta mines nau ka man gyat kijiye math counting me sawal ko solve? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Kos theeta barabar 2/3 tab 2g squire theeta plus 2 10 squire theeta mines nau ka man gyat kijiye math counting me sawal ko solve? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Kos theeta barabar 2/3 tab 2g squire theeta plus 2 10 squire theeta mines nau ka man gyat kijiye math counting me sawal ko solve?.
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