Question
Download Solution PDFयदि b sin θ = a है, तो sec θ + tan θ = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
b sin θ= a
प्रयुक्त अवधारणा:
sin θ= लंब/कर्ण
sec θ= कर्ण/आधार
tan θ= लंब/आधार
गणना:
b sin θ=a
sin θ= a/b
इसलिए, लंब = a और कर्ण = b
(कर्ण)2 = (लंब)2 + (आधार)2
b2 = a2 + आधार2
आधार2 = b2 - a2
\(base = {\sqrt{b^2-a^2} }\)
secθ = कर्ण/आधार = b/\({ \sqrt{b^2-a^2} }\)
tanθ = लंब/आधार = a/\({ \sqrt{b^2-a^2} }\)
इसलिए, secθ+ tanθ = b/\({ \sqrt{b^2-a^2} }\)+ (a/\({ \sqrt{b^2-a^2} }\))
secθ + tanθ = (b+ a)/ (\({ \sqrt{b^2-a^2} }\))
∵ (b + a) = √(b + a) × √(b + a)
⇒ sec θ + tan θ = \( {√{(b+a)(b+a)} }\)/ \( { √{(b-a)(b+a)} }\)
sec θ+ tan θ= \(√ {\frac{{b + a}}{{b - a}}} \)
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