Question
Download Solution PDFযদি tan A + cot A = 2 হয়, তাহলে 2(tan2 A + cot2 A) এর মান নির্ণয় করুন।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
tan A + cot A = 2
গণনা:
প্রশ্নানুসারে,
আমাদের আছে, tan A + cot A = 2
উভয়পক্ষকে বর্গ করে পাই,
⇒ (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
অতএব,
2(tan2 A + cot2 A) = 2 × 2
⇒ 4
∴ 2(tan2 A + cot2 A) এর মান হল 4
Shortcut Trickআমরা মান নির্ণয় পদ্ধতির সাথে যেতে পারি,
যদি আমরা A = 45° রাখি তবে এটি tan A + cot A = 2 সমীকরণকে সন্তুষ্ট করে, তাই
2(tan2 A + cot2 A)
⇒ 2(1 + 1)
⇒ 4
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