Question
Download Solution PDFΔABC में, AB = 20 सेमी, BC = 21 सेमी और AC = 29 सेमी है, तो cot C + cosec C - 2tan A का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
AB = 20 सेमी
BC = 21 सेमी
AC = 29 सेमी
प्रयुक्त अवधारणा:
पाइथागोरस प्रमेय कहती है कि "एक समकोण त्रिभुज में, कर्ण भुजा का वर्ग अन्य दो भुजाओं के वर्गों के योग के बराबर होता है।
गणना:
पाइथागोरस प्रमेय का उपयोग करने पर,
AC2 = AB2 + BC2
⇒ 292 = 202 + 212
ΔABC एक समकोण त्रिभुज है।
⇒ cot C = BC/AB = 21/20
⇒ cosec C = AC/AB = 29/20
⇒ tan A = BC/AB = 21/20
cot C + cosec C - 2tan A = 21/20 + 29/20 - 2 × 21/20
⇒ 8/20
⇒ 2/5
अतः cot C + cosec C - 2tan A का मान = 2/5
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