Question
Download Solution PDFयदि sinθ + cosθ = √3 है, तो tanθ + cotθ का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
sinθ + cosθ = √3
हमें tanθ + cotθ का मान ज्ञात करना है।
प्रयुक्त अवधारणा:
त्रिकोणमितीय सर्वसमिकाओं का उपयोग करें:
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(sinθ + cosθ)2 = sin2θ + cos2θ + 2sinθcosθ
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sin2θ + cos2θ = 1
गणना:
चरण 1: (sinθ + cosθ)2 का प्रसार करें:
√32 = sin2θ + cos2θ + 2sinθ cosθ
⇒ 3 = 1 + 2sinθ cosθ
⇒ 2sinθ cosθ = 2
⇒ sinθ cosθ = 1
चरण 2: सर्वसमिका tanθ + cotθ का उपयोग करें:
tanθ + cotθ = (sinθ/cosθ) + (cosθ/sinθ)
⇒ tanθ + cotθ = (sin2θ + cos2θ) / (sinθcosθ)
⇒ tanθ + cotθ = 1 / 1
⇒ tanθ + cotθ = 1
निष्कर्ष:
∴ tanθ + cotθ का मान 1 है।
सही उत्तर विकल्प 3 है।
Last updated on Jul 1, 2025
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