IBPS RRB Office Assistant (Multipurpose) Prelims practice question
If tan 3A = cot(A + 10°), where 3A and A + 10° are acute angles, find A.
From a IBPS RRB Office Assistant (Multipurpose) Prelims Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (C) 20°
cot(A + 10°) = tan(90° − (A + 10°)). So 3A = 90° − (A + 10°) ⇒ 4A = 90° − 10° = 80° ⇒ A = 20°. (Setting 3A equal to A + 10° directly is the trap — the two ratios are co-functions, so the angles are complementary, not equal.)
हिंदी में प्रश्न
यदि tan 3A = cot(A + 10°) है, जहाँ 3A और A + 10° न्यून कोण हैं, तो A ज्ञात कीजिए।
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सही उत्तर: (C) 20°
cot(A + 10°) = tan(90° − (A + 10°))। अतः 3A = 90° − (A + 10°) ⇒ 4A = 90° − 10° = 80° ⇒ A = 20°। (3A को सीधे A + 10° के बराबर रख देना गलत है — दोनों अनुपात सह-फलन हैं, अतः कोण पूरक हैं, बराबर नहीं।)
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