CBSE Class 11-science Answered
If A+B+C=pi , then equality of equation
(1/2)(cosA cosB + cosB cosC + cosC cosA)
must hold:
a) <= 3/2. b) >=(-3) c) <=3/8 d) >=(-1)
Asked by shanujam03 | 03 Oct, 2020, 08:59: PM
Expert Answer
Given: A+B+C=pi
Consider,
(1/2)(cosA cosB + cosB cosC + cosC cosA)
= (1/4)(2cosA cosB + 2cosB cosC + 2cosC cosA)
= (1/4)[(cosA + cosB + cosC)2 - (cos2A + cos2B + cos2C)]
>= (1/4)[1 - (cos2A + cos2B + cos2C)]
As (cosA + cosB + cosC)2 >= 1
Use this inequality and get the inequality for (1/2)(cosA cosB + cosB cosC + cosC cosA)
Answered by Renu Varma | 06 Oct, 2020, 10:52: AM
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