Question
Download Solution PDF7cos2θ + 5sin2θ का अधिकतम मान क्या होगा?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFगणना:
माना कि f(θ) = 7cos2θ + 5sin2θ
= 2cos2θ + 5cos2θ + 5sin2θ
= 2cos2θ + 5(cos2θ + sin2θ)
= 2cos2θ + 5 [∵ cos2θ + sin2θ = 1]
जैसा कि हम जानते हैं कि, 0 ≤ cos2θ ≤ 1
⇒ 0 ≤ 2cos2θ ≤ 2
⇒ 0 + 5 ≤ 2cos2θ + 5 ≤ 2 + 5
⇒ 5 ≤ 2cos2θ + 5 ≤ 7
⇒ 5 ≤ f(θ) ≤ 7
इस प्रकार,फलन का अधिकतम मान 7 है।
Alternate Method
संकल्पना:
यदि acos2θ + bsin2θ है, जहाँ, a > b
a अधिकतम मान होगा और b न्यूनतम मान होगा।
गणना:
7cos2θ + 5sin2θ
संकल्पना के अनुसार
acos2θ + bsin2θ जहाँ, a > b
तुलना करने पर
⇒ a = 7, b = 5 जहाँ, 7 > 5
∴ 7cos2θ + 5sin2θ का अधिकतम मान 7 है।
Last updated on Jun 26, 2025
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