RRB Technician Grade 3 previous year question
If cotθ = 1/√3, (0° < θ < 90°), then the value of (2 − sin²θ)/(1 + cos²θ) + cosec²θ − sec²θ is:
Asked in RRB Technician Grade 3 (10 Mar 2026 Shift 2) · Quantitative Aptitude
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Correct answer: (C) −5/3
cot θ = 1/√3 gives θ = 60°, so sin²θ=3/4 and cos²θ=1/4, giving cosec²θ=4/3 and sec²θ=4. Then (2−3/4)/(1+1/4) + 4/3 − 4 = 1 + 4/3 − 4 = −5/3.
हिंदी में प्रश्न
यदि cotθ = 1/√3, (0° < θ < 90°) है, तो (2 − sin²θ)/(1 + cos²θ) + cosec²θ − sec²θ का मान ज्ञात कीजिए।
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सही उत्तर: (C) −5/3
cot θ = 1/√3 से θ = 60° प्राप्त होता है, अतः sin²θ=3/4, cos²θ=1/4, cosec²θ=4/3, sec²θ=4 है। तब (2−3/4)/(1+1/4) + 4/3 − 4 = 1 + 4/3 − 4 = −5/3 प्राप्त होता है।
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