Question
Download Solution PDFजर sin x + cos x = √2 sin x असेल, तर sin x - cos x चे मूल्य काढा:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले आहे:
sin x + cos x = √2 sin x
वापरलेले सूत्र:
त्रिकोणमितीय नियम आणि अंकगणितीय प्रक्रिया
a2 - b2 = (a - b) × (a + b)
गणना:
दिलेल्या समीकरणापासून सुरुवात करू:
sin x + cos x = √2 sin x
दोन्ही बाजूंचा वर्ग करू
(sin x + cos x)2 = (√ 2sinx)2
⇒ sin2x + cos2x + 2sinxcosx = 2sin2x
⇒ 2sinxcosx = sin2x - cos2x
⇒ 2sinxcosx = (sinx - cosx) x (sin x + cos x)
⇒ 2sinxcosx = (sinx - cosx) x √ 2sinx
⇒ √ 2cosx = (sinx - cosx)
पर्याय 4 योग्य आहे.
Last updated on Jun 17, 2025
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