Question
Download Solution PDFजर cot A + cos A = m आणि cot A – cos A = n असेल, तर:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेल्याप्रमाणे:
cot A + cos A = m
cot A – cos A = n
वापरलेली संकल्पना:
(a + b)2 = a2 + b2 + 2ab
(a – b)2 = a2 + b2 – 2ab
गणना:
cot A + cos A = m च्या दोन्ही बाजूंचे वर्ग करू,
⇒ m2 = cot2A + cos2A + 2cotA cosA
cot A – cos A = n च्या दोन्ही बाजूंचे वर्ग करू,
⇒ n2 = cot2A + cos2A – 2cotA cosA
⇒ m2 – n2 = cot2A + cos2A + 2cotA cosA – (cot2A + cos2A – 2cotA cosA)
⇒ m2 – n2 = 4cotA cosA
दोन्ही बाजूंचे वर्ग केल्यास, आपल्याला मिळेल
⇒ (m2 – n2)2 = 16cot2A cos2A --- (1)
⇒ m×n = (cot A + cos A)(cot A – cos A)
⇒ mn = cot2 A - cos2 A = (cos2 A / sin2 A) - cos2 A
⇒ mn = (cos2 A - cos2 A sin2 A)/sin2 A
⇒ mn = cos2 A(1 - sin2 A)/sin2 A
⇒ mn = cot2 A cos2 A
समीकरण (1) मध्ये, cot2 A cos2 A = mn ठेवल्यास, आपल्याला मिळेल
⇒ (m2 – n2)2 = 16mn
म्हणून, योग्य पदावली (m2 - n2)2 = 16 mn आहे.
Last updated on Jul 18, 2025
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