Test:209 QNo:4

sin(cos(a))=a and cos(sin(b))=b
Then:

3 Answers

cos(a) < 2pi+[pi/2 - sin(b)] ........... [ for all val of a and b ]

sin(cos a) < cos(sin b )

a < b

Why is it that cos(a) < 2pi+[pi/2 - sin(b)] ........... [ for all val of a and b ]?
Where does pi/2 - sinb come from?

RHS is greater than 2pi (as pi/2-sinx >0 for all x )
just apply sin on both sides of first statement you will see imp of pi/2-sinb,,,

very neat trick indeed..
When i did the question i used graphs..

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