Really Real Numbers!

Algebra Level 4

aa and bb are two real numbers. Read the following statements about them.

[1].[1]. If a>ba>b and none of them are equal to zero, then 1a<1b\dfrac{1}{a}<\dfrac{1}{b}.

[2][2]. The equation sin1(a)+cos1(a)=π2\sin^{-1} (a)+\cos^{-1} (a)=\dfrac{\pi}{2} holds for all real numbers aa.

[3][3]. ab\dfrac{a}{b} is always a real number.

Which of these statements are true?

Details and assumptions:

The statements are independent. That means if according to statement [1][1], a=2a=2; it applies to statement [1][1] only.

This problem is from the set "MCQ Is Not As Easy As 1-2-3". You can see the rest of the problems here.


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