Which of the following inequalities are ...

Which of the following inequalities are valid- `|tan^-1 x-tan^-1y|<= |x-y|AA x,y in R`

`|tan^(-1)x-tan^(-1)y| le |x-y| AA x, y in R`

`|tan^(-1)x-tan^(-1)y| ge |x-y|`

`|sin x- sin y| le |x-y|`

`|sin x- sin y| ge |x-y|`

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The correct Answer is:

A, C

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The solution of which of the following differential equations is tan^(-1)x+tan^(-1)y=c ?

`dy/dx=(1+y^2)/(1+x^2)`

`(1+x^2)dy+(1+y^2)dx=0`

`dy/dx=(1+x^2)/(1+y^2)`

`(1+x^2)dx+(1+y^2)dy=0`

`(x+y)/(tan1)=-2`

`(tan^(-1)x)/(1-tan^(-1)y)=2`

`(x+y)/(tan1)=2`

`(x+y)/(cot1)=1`