Maths-
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Question

In a triangle ABC

  1. sin invisible function application A over 2 sin invisible function application B over 2 sin invisible function application C over 2 less or equal than 1 over 8
  2. sin invisible function application A over 2 sin invisible function application B over 2 sin invisible function application C over 2 less than 1 over 8
  3. sin invisible function application A over 2 sin invisible function application B over 2 sin invisible function application C over 2 greater than 1 over 8
  4. sin invisible function application A over 2 sin invisible function application B over 2 sin invisible function application C over 2 greater or equal than 1 over 8

Hint:

As we know that GMless or equal than AM, from this we can write that open parentheses sin squared A over 2. sin squared B over 2. sin squared C over 2 close parentheses to the power of 1 third end exponent less or equal than fraction numerator sin squared A over 2 plus sin squared B over 2 plus sin squared C over 2 over denominator 3 end fraction. Also, sin squared A over 2 plus sin squared B over 2 plus sin squared C over 2 greater or equal than 3 over 4 from both these we can determine the true statement from the following.

The correct answer is: sin invisible function application A over 2 sin invisible function application B over 2 sin invisible function application C over 2 less or equal than 1 over 8


    We know that GMless or equal than AM,
    open square brackets sin squared A over 2. sin squared B over 2. sin squared C over 2 close square brackets to the power of 1 third end exponent less or equal than fraction numerator sin squared begin display style A over 2 end style plus sin squared begin display style B over 2 end style plus sin squared begin display style C over 2 end style over denominator 3 end fraction
A l s o comma space sin squared A over 2 plus sin squared B over 2 plus sin squared C over 2 greater or equal than 3 over 4
open square brackets sin squared A over 2. sin squared B over 2. sin squared C over 2 close square brackets to the power of 1 third end exponent less or equal than 1 third cross times 3 over 4
rightwards double arrow sin squared A over 2. sin squared B over 2. sin squared C over 2 less or equal than open parentheses 1 fourth close parentheses cubed
rightwards double arrow open parentheses sin A over 2. sin B over 2. sin C over 2 close parentheses squared less or equal than 1 over 64
rightwards double arrow sin A over 2. sin B over 2. sin C over 2 less or equal than 1 over 8

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