Question
Download Solution PDF27 tan2x + 3cot2x का न्यूनतम मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
समांतर माध्य, ज्यामितीय माध्य, हरात्मक माध्य के सूत्र:
यदि A संख्या a और b का समांतर माध्य है
⇔
यदि G संख्या a और b का ज्यामितीय माध्य है
⇔
समांतर माध्य (AM) और ज्यामितीय माध्य (GM) के बीच संबंध
AM ≥ GM
गणना:
दिया गया है कि,
27 tan2x + 3cot2x
माना a = 27tan2 x, b = 3cot2 x
हम जानतें है कि,
AM ≥ GM
हम जानतें है कि, tan θ × cot θ = 1
⇒ 27 tan2x + 3cot2x ≥ 18
⇒ 27 tan2x + 3cot2x ∈ [18, ∞)
अत: न्यूनतम मान 18 है।
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