Question
Download Solution PDFजर tan A + cot A = 2 असेल, तर 2 (tan2 A + cot2 A) चे मूल्य आहे:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेल्यानुसार:
tan A + cot A = 2
गणना:
प्रश्नानुसार,
आपल्याकडे tan A + cot A = 2 आहे
दोन्ही बाजूंचा वर्ग केल्यावर आपल्याला मिळते
⇒ (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
आता,
2(tan2 A + cot2 A) = 2 × 2
⇒ 4
∴ 2 (tan2 A + cot2 A) चे मूल्य 4 आहे.
Shortcut Trick
त्यात मूल्य ठेवण्याच्या पद्धतीसह जाऊ शकतो,
जर आपण A = 45° ठेवले तर ते tan A + cot A = 2 या समीकरणाचे समाधान करते, म्हणून
2(tan2 A + cot2 A)
⇒ 2(1 + 1)
⇒ 4
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