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

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 1)

Answer 1

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)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= \(√ {\frac{{b + a}}{{b - a}}} \)