Q. 95.0( 2 Votes )

The value of 2 sin can be a +, where a is a positive number and a1.

Answer :

False

Given: ‘a’ is a positive number and a≠1


AM > GM


(Arithmetic Mean (AM) of a list of non- negative real numbers is greater than or equal to the Geometric mean (GM) of the same list)


If a and b be such numbers, then


and GM = √ab


By assuming that statement is be true.


Similarly, AM and GM of a and 1/a are (a+1/a)/2 and √(a.1/a) respectively.


By property, (a+1/a)/2 > √(a.1/a)



2 sin θ > 2 (By our assumption)


sin θ > 1


But -1 ≤ sin θ ≤ 1


Our assumption is wrong and that 2 sin θ cannot be equal to


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