Question
Download Solution PDFयदि 2 cot θ = 3 है, तो \(\frac{\sqrt{13} \sin \theta-3 \tan \theta}{3 \tan \theta+\sqrt{13} \cos \theta}\) का मान ज्ञात कीजिये।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
2cotθ = 3
प्रयुक्त सूत्र:
Sinθ = P/H
Cosθ = B/H
Tanθ = P/B
Cotθ = B/P
H2 = P2 + B2
जहाँ P = कर्ण
B = आधार
H = ऊँचाई
गणना:
2cotθ = 3
⇒ cotθ = 3/2
(Cotθ = B/P) से तुलना करने पर, हमें प्राप्त होता है
⇒ B = 3
⇒ P = 2
पाइथागोरस प्रमेय के अनुसार
⇒ H2 = P2 + B2
⇒ H2 = 22 + 32
⇒ H = √13
⇒ Sinθ = 2/√13
⇒ Cosθ = 3/√13
⇒ Tanθ = 2/3
दिए गए समीकरण में सभी मानों को रखने पर:
\(\frac{\sqrt{13} \sin \theta-3 \tan \theta}{3 \tan \theta+\sqrt{13} \cos \theta}\)= (√13 * 2/√13 - 3 * 2/3 )/ (3 * 2/3 + √13 * 3/√13)
⇒ (2 - 2)/(2 + 3)
⇒ 0
व्यंजक का मान 0 है।
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