Question
Download Solution PDFఒకవేళ tan A + cot A = 2, అయితే, అప్పుడు 2(tan2 A + cot2 A) యొక్క విలువ ఎంత:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఇచ్చింది:
tan A + cot A = 2
గణన:
ప్రశ్న ప్రకారం.
మనకు tan A + cot A = 2 ఉంది
రెండు వైపులా వర్గం చేస్తే, మనకు లభిస్తుంది
⇒ (tan A + cot A)2 = (2)2
⇒ tan2 A + cot2 A + 2(tan A)(cot A) = 4
⇒ tan2 A + cot2 A + 2(tan A)(1/tan A) = 4
⇒ tan2 A + cot2 A + 2 = 4
⇒ tan2 A + cot2 A = 2
ఇప్పుడు
2(tan2 A + cot2 A) = 2 × 2
⇒ 4
∴ 2(tan2 A + cot2 A) విలువ 4.
Shortcut Trick
మనం విలువలను ప్రతిక్షేపించే పద్ధతితో వెళ్లవచ్చు,
ఒకవేళ మనం A = 45° అని ప్రతిక్షేపిస్తే, అది tan A + cot A = 2 అనే సమీకరణాన్ని సంతృప్తిపరుస్తుంది, కాబట్టి
2(tan2 A + cot2 A)
⇒ 2(1 + 1)
⇒ 4
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