यदि b sin θ = a है, तो sec θ + tan θ = ?

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SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 1)
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  1. \(\sqrt {\frac{{b + a}}{{b - a}}} \)
  2. \(\sqrt {\frac{{1}}{{b + a}}} \)
  3. \(\sqrt {\frac{{1}}{{b - a}}} \)
  4. \(\sqrt {\frac{{b - a}}{{b + a}}} \)

Answer (Detailed Solution Below)

Option 1 : \(\sqrt {\frac{{b + a}}{{b - a}}} \)
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Detailed Solution

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दिया 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)= (लंब)+ (आधार)2

b= aआधार2

आधार= b-  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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