Question
Download Solution PDFमान लीजिए समीकरण sec x.cosec x = p का एक हल है, जहाँ p एक धनात्मक वास्तविक संख्या है। p का लघुतम मान क्या होगा?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFइस्तेमाल किया गया सूत्र:
sec x =
(sin x - cos x)2 = sin2 x + cos2 x - 2 sin x cos x
sin2 x + cos2 x = 1, tan x =
गणना:
हमारे पास sec x × cosec x = p है
⇒
⇒ sinx.cos x =
हम जानते हैं कि,
(sin x - cos x)2 = sin2 x + cos2 x - 2 sin x cos x
(i) से हमें प्राप्त होता है
⇒ (sin x - cos x)2 = 1 - 2 ×
हम जानते हैं कि किसी भी संख्या का वर्ग ≥ 0 होता है
(sin x - cos x)2 ≥ 0
(ii) से हमें प्राप्त होता है
⇒ 1 ≥ 2/p
⇒ 1/1 ≤ p/2
⇒ p ≥ 2
∴ p का सबसे छोटा मान 2 है।
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