Question
Download Solution PDFयदि sin x + cos x = √2 sin x है, तो sin x - cos x का मान कितना है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
sin x + cos x = √2 sin x
प्रयुक्त सूत्र:
त्रिकोणमितीय सर्वसमिकाएँ और बीजगणितीय जोड़-तोड़।
a2 - b2 = (a - b) x (a + b)
गणना:
दिए गए समीकरण से शुरू करते हैं:
sin x + cos x = √2 sin x
दोनों पक्षों का वर्ग करने पर
(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)
सही उत्तर विकल्प 4 है।
Last updated on Jun 17, 2025
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